Françoise Tisseur

Structured condition numbers and backward errors in scalar product spaces, Electron (2008)

Mims Eprint, Michael Karow, Michael Karow, Daniel Kressner, Daniel Kressner, Françoise Tisseur, ...

Abstract. This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to...

Mims Eprint, Françoise Tisseur, Françoise Tisseur, Stef Graillat, Stef Graillat

Abstract. We investigate the effect of structure-preserving perturbations on the solution to a linear system, matrix inversion, and distance to singularity. Particular attention is paid to linear and...

Structured tools for structured matrices (2008)

D. Steven Mackey, Niloufer Mackey, Françoise Tisseur

Abstract. An extensive and unified collection of structure-preserving transformations is presented and organized for easy reference. The structures involved arise in the context of a nondegenerate...

Functions preserving matrix groups and iterations for the matrix square root (2008)

Françoise Tisseur, Mims Eprint, Nicholas J. Higham, Nicholas J. Higham, D. Steven Mackey, D. Steven Mackey, ...

Abstract. For which functions f does A ∈ G ⇒ f(A) ∈ G when G is the matrix automorphism group associated with a bilinear or sesquilinear form? For example, if A is symplectic when is f(A)...

Computing the polar decomposition and the matrix sign decomposition in matrix groups (2008)

Françoise Tisseur, Mims Eprint, Nicholas J. Higham, Nicholas J. Higham, D. Steven Mackey, D. Steven Mackey, ...

Abstract. For any matrix automorphism group G associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of A ∈ G...

Structured condition numbers and backward errors in scalar product spaces, Electron (2008)

Françoise Tisseur, Stef Graillat

Abstract. We investigate the effect of structure-preserving perturbations on the solution to a linear system, matrix inversion, and distance to singularity. Particular attention is paid to linear and...

Michael Karow, Daniel Kressner, Françoise Tisseur

Abstract. This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to...

Structured mapping problems for matrices associated with scalar products. part II: Automorphism groups (2008)

Mims Eprint, D. Steven Mackey, D. Steven Mackey, Niloufer Mackey, Niloufer Mackey, Françoise Tisseur, ...

Abstract. Given a class of structured matrices S, we identify pairs of vectors x, b for which there exists a matrix A ∈ S such that Ax = b, and also characterize the set of all matrices A ∈ S...

Michael Karow, Daniel Kressner, Françoise Tisseur

Abstract. This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to...

Michael Karow, Daniel Kressner, Françoise Tisseur

Abstract. This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to...

Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems (2008)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise, Garvey, Seamus D.

The most common way of solving the quadratic eigenvalue problem (QEP) $(\l^2 M + \l D + K)x=0$ is to convert it into a linear problem $(\l X + Y)z=0$ of twice the dimension and solve the linear...

AN IMPROVED ARC ALGORITHM FOR DETECTING DEFINITE HERMITIAN PAIRS ∗ (2008)

Chun-hua Guo, Nicholas J. Higham, Françoise Tisseur, Mims Eprint, Chun-hua Guo, Nicholas J. Higham, ...

Abstract. A 25-year old and somewhat neglected algorithm of Crawford and Moon attempts to determine whether a given Hermitian matrix pair (A, B) is definite by exploring the range of the function...

Definite matrix polynomials and their linearization by definite pencils (2008)

Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur, Mims Eprint, Nicholas J. Higham, D. Steven Mackey, ...

Abstract. Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral...

A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra (2007)

Nicholas J. Higham, Françoise Tisseur

. The matrix 1-norm estimation algorithm used in LAPACK and various other software libraries and packages has proved to be a valuable tool. However, it has the limitations that it offers the user no...

Linear Algebra and its Applications 351–352 (2002) 435–453 (2007)

Nicholas J. Higham, Françoise Tisseur

www.elsevier.com/locate/laa More on pseudospectra for polynomial eigenvalue problems and applications in control theory �

Structured Tools For Structured Matrices (2007)

D. Steven Mackey, Steven Mackey Niloufer, Françoise Tisseur

We present an extensive and unified collection of structure-preserving transformations, organized for easy reference. The structures we work with arise in the context of a nondegenerate bilinear or...

Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems (2007)

Guo, Chun-Hua, Higham, Nicholas J., Tisseur, Françoise

Hyperbolic quadratic matrix polynomials $Q(\lambda) = \lambda^2 A + \lambda B + C$ are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics...

Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems (2007)

Guo, Chun-Hua, Higham, Nicholas J., Tisseur, Françoise

Hyperbolic quadratic matrix polynomials $Q(\lambda) = \lambda^2 A + \lambda B + C$ are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics...

Notes on Hyperbolic Matrix Polynomials and Definite Linearizations (2007)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise

Definite Matrix Polynomials and their Linearization by Definite Pencils (2007)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise

Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that...

Definite Matrix Polynomials and their Linearization by Definite Pencils (2007)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise

Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that...

Definite Matrix Polynomials and their Linearization by Definite Pencils (2007)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise

Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that...

Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras (2007)

Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

Given a class of structured matrices $\Sb$, we identify pairs of vectors $x,b$ for which there exists a matrix $A\in\Sb$ such that $Ax=b$, and also characterize the set of all matrices $A\in\Sb$...

Backward Error of Polynomial Eigenproblems Solved by Linearization (2007)

Higham, Nicholas J., Li, Ren-Cang, Tisseur, Françoise

The most widely used approach for solving the polynomial eigenvalue problem $P(\lambda)x = \bigl(\sum_{i=0}^m \l^i A_i\bigr) x = 0$ in $n\times n$ matrices $A_i$ is to linearize to produce a larger...

Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems (2007)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise, Garvey, Seamus D.

The most common way of solving the quadratic eigenvalue problem (QEP) $(\l^2 M + \l D + K)x=0$ is to convert it into a linear problem $(\l X + Y)z=0$ of twice the dimension and solve the linear...

Backward Error of Polynomial Eigenproblems Solved by Linearization (2007)

Higham, Nicholas J., Li, Ren-Cang, Tisseur, Françoise

The most widely used approach for solving the polynomial eigenvalue problem $P(\lambda)x = \bigl(\sum_{i=0}^m \l^i A_i\bigr) x = 0$ in $n\times n$ matrices $A_i$ is to linearize to produce a larger...

Backward Error of Polynomial Eigenproblems Solved by Linearization (2007)

Higham, Nicholas J., Li, Ren-Cang, Tisseur, Françoise

The most widely used approach for solving the polynomial eigenvalue problem $P(\lambda)x = \bigl(\sum_{i=0}^m \l^i A_i\bigr) x = 0$ in $n\times n$ matrices $A_i$ is to linearize to produce a larger...

ON THE DEFINITION OF TWO NATURAL CLASSES OF SCALAR PRODUCT ∗ (2007)

D. Steven Mackey, Niloufer Mackey, Francoise Tisseur, Mims Eprint, D. Steven Mackey, Niloufer Mackey, ...

Abstract. We identify two natural classes of scalar product, termed unitary and orthosymmetric, which serve to unify assumptions for the existence of structured factorizations, iterations and...

Detecting and solving hyperbolic quadratic eigenvalue problems (2007)

Chun-hua Guo, Nicholas J. Higham, Françoise Tisseur, Mims Eprint, Chun-hua Guo, Nicholas J. Higham, ...

Abstract. Hyperbolic quadratic matrix polynomials Q(λ) = λ 2 A + λB + C are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are...

Detecting and solving hyperbolic quadratic eigenvalue problems (2007)

Chun-hua Guo, Nicholas J. Higham, Françoise Tisseur, Mims Eprint, Chun-hua Guo, Nicholas J. Higham, ...

Abstract. Hyperbolic quadratic matrix polynomials Q(λ) = λ 2 A + λB + C are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are...

Structured Eigenvalue Condition Numbers (2006)

Karow, Michael, Kressner, Daniel, Tisseur, Françoise

This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that...

Structured Eigenvalue Condition Numbers (2006)

Karow, Michael, Kressner, Daniel, Tisseur, Françoise

This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that...

Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems (2006)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise, Garvey, Seamus D.

The most common way of solving the quadratic eigenvalue problem (QEP) $(\l^2 M + \l D + K)x=0$ is to convert it into a linear problem $(\l X + Y)z=0$ of twice the dimension and solve the linear...

Symmetric Linearizations for Matrix Polynomials (2006)

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

A standard way of treating the polynomial eigenvalue problem $P(\l)x = 0$ is to convert it into an equivalent matrix pencil---a process known as linearization. Two vector spaces of pencils...

Backward Error of Polynomial Eigenproblems Solved by Linearization (2006)

Higham, Nicholas J., Li, Ren-Cang, Tisseur, Françoise

The most widely used approach for solving the polynomial eigenvalue problem $P(\lambda)x = \bigl(\sum_{i=0}^m \l^i A_i\bigr) x = 0$ in $n\times n$ matrices $A_i$ is to linearize to produce a larger...

Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras (2006)

Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

Given a class of structured matrices $\Sb$, we identify pairs of vectors $x,b$ for which there exists a matrix $A\in\Sb$ such that $Ax=b$, and also characterize the set of all matrices $A\in\Sb$...

Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras (2006)

Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

Given a class of structured matrices $\Sb$, we identify pairs of vectors $x,b$ for which there exists a matrix $A\in\Sb$ such that $Ax=b$, and also characterize the set of all matrices $A\in\Sb$...

Structured Eigenvalue Condition Numbers (2006)

Karow, Michael, Kressner, Daniel, Tisseur, Françoise

This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that...

Structured Condition Numbers and Backward Errors in Scalar Product Spaces (2006)

Tisseur, Françoise, Graillat, Stef

We investigate the effect of structure-preserving perturbations on the solution to a linear system, matrix inversion, and distance to singularity. Particular attention is paid to linear and nonlinear...

Symmetric Linearizations for Matrix Polynomials (2006)

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

A standard way of treating the polynomial eigenvalue problem $P(\l)x = 0$ is to convert it into an equivalent matrix pencil---a process known as linearization. Two vector spaces of pencils...

The Conditioning of Linearizations of Matrix Polynomials (2006)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise

The standard way of solving the polynomial eigenvalue problem of degree $m$ in $n\times n$ matrices is to ``linearize'' to a pencil in $mn\times mn$ matrices and solve the generalized eigenvalue...

Symmetric Linearizations for Matrix Polynomials (2006)

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

A standard way of treating the polynomial eigenvalue problem $P(\l)x = 0$ is to convert it into an equivalent matrix pencil---a process known as linearization. Two vector spaces of pencils...

Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems (2006)

Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur, Seamus D. Garvey, Mims Eprint, Nicholas J. Higham, ...

The most common way of solving the quadratic eigenvalue problem (QEP) (λ 2 M +λD+K)x = 0 is to convert it into a linear problem (λX +Y)z = 0 of twice the dimension and solve the linear problem by...

Backward error of polynomial eigenproblems solved by linearization (2006)

Nicholas J. Higham, Ren-cang Li, Françoise Tisseur, Mims Eprint, Nicholas J. Higham, Ren-cang Li, ...

Abstract. The most widely used approach for solving the polynomial eigenvalue problem P(λ)x = ��m i=0 λi � Ai x =0inn × n matrices Ai is to linearize to produce a larger order pencil L(λ)...

Symmetric linearizations for matrix polynomials (2006)

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey, Françoise Tisseur, Mims Eprint, Nicholas J. Higham, ...

Abstract. A standard way of treating the polynomial eigenvalue problem P(λ)x = 0 is to convert it into an equivalent matrix pencil—a process known as linearization. Two vector spaces of pencils...

And by contacting: The MIMS Secretary (2006)

Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur, Seamus D. Garvey, Mims Eprint, Nicholas J. Higham, ...

Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems

Symmetric linearizations for matrix polynomials (2006)

Françoise Tisseur, Mims Eprint, Nicholas J. Higham, Nicholas J. Higham, D. Steven Mackey, D. Steven Mackey, ...

Abstract. A standard way of treating the polynomial eigenvalue problem P(λ)x = 0 is to convert it into an equivalent matrix pencil—a process known as linearization. Two vector spaces of pencils...

Symmetric Linearizations for Matrix Polynomials (2005)

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

A standard way of treating the polynomial eigenvalue problem $P(\l)x = 0$ is to convert it into an equivalent matrix pencil---a process known as linearization. Two vector spaces of pencils...

The Conditioning of Linearizations of Matrix Polynomials (2005)

Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise

The standard way of solving the polynomial eigenvalue problem of degree $m$ in $n\times n$ matrices is to ``linearize'' to a pencil in $mn\times mn$ matrices and solve the generalized eigenvalue...

The Ehrlich--Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue Problem (2005)

Bini, Dario A., Gemignani, Luca, Tisseur, Françoise

An algorithm based on the Ehrlich--Aberth iteration is presented for the computation of the zeros of $p(\lambda)=\det(T-\lambda I)$, where $T$ is a real irreducible nonsymmetric tridiagonal matrix....

Functions Preserving Matrix Groups and Iterations for the Matrix Square Root (2005)

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

For any matrix automorphism group $\G$ associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of $A\in\G$ also lie...

Functions Preserving Matrix Groups and Iterations for the Matrix Square Root (2005)

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

For any matrix automorphism group $\G$ associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of $A\in\G$ also lie...

The conditioning of linearizations of matrix polynomials (2005)

Mims Eprint, Nicholas J. Higham, Nicholas J. Higham, D. Steven Mackey, D. Steven Mackey, Françoise Tisseur, ...

Abstract. The standard way of solving the polynomial eigenvalue problem of degree m in n × n matrices is to “linearize ” to a pencil in mn × mn matrices and solve the generalized eigenvalue...

The conditioning of linearizations of matrix polynomials (2005)

Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur

Abstract. The standard way of solving the polynomial eigenvalue problem of degree m in n ×n matrices is to “linearize ” to a pencil in mn ×mn matrices and solve the generalized eigenvalue...

Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups (2004)

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

For any matrix automorphism group $\G$ associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of $A\in\G$ also lie...

Tridiagonal-diagonal reduction of symmetric indefinite pairs (2004)

Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups (2004)

We consider the reduction of a symmetric indefinite matrix pair (A,B), with B nonsingular, to tridiagonal-diagonal form by congruence transformations. This is an important reduction in solving...

Higham, Nicholas J., Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

For any matrix automorphism group $\G$ associated with a bilinear or sesquilinear form, Mackey, Mackey, and Tisseur have recently shown that the matrix sign decomposition factors of $A\in\G$ also lie...

G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces (2004)

Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

We characterize the analogues of Householder transformations in matrix groups associated with scalar products, and precisely delimit their mapping capabilities: given a matrix group Image and vectors...

Structured factorizations in scalar product spaces (2004)

D. Steven Mackey, Niloufer Mackey, Françoise Tisseur

Abstract. Let A belong to an automorphism group, Lie algebra or Jordan algebra of a scalar product. When A is factored, to what extent do the factors inherit structure from A? We answer this question...

Structured factorizations in scalar product spaces (2004)

D. Steven Mackey, Niloufer Mackey, Françoise Tisseur

Abstract. Let A belong to an automorphism group, Lie algebra, or Jordan algebra of a scalar product. When A is factored, to what extent do the factors inherit structure from A? We answer this...

A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems (2003)

Structured tools for structured matrices (2003)

We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to...

Mackey, D. Steven, Mackey, Niloufer, Tisseur, Françoise

An extensive and unified collection of structure-preserving transformations is presented and organized for easy reference. The structures involved arise in the context of a non-degenerate bilinear or...

Perturbation theory for homogeneous polynomial eigenvalue problems (2003)

Tisseur, Françoise, Dedieu, Jean-Pierre

We consider polynomial eigenvalue problems P(A,alpha,beta)x=0 in which the matrix polynomial is homogeneous in the eigenvalue (alpha,beta)&unknown;C2. In this framework infinite eigenvalues are on...

Simultaneous tridiagonalization of two symmetric matrices (2003)

Garvey, Seamus D., Tisseur, Françoise, Friswell, Michael I., Penny, John E. T., Prells, Uwe

We show how to simultaneously reduce a pair of symmetric matrices to tridiagonal form by congruence transformations. No assumptions are made on the non-singularity or definiteness of the two...

Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra (2003)

Dedieu, Jean-Pierre, Kim, Myong-Hi, Shub, Michael, Tisseur, Françoise

Let g : E → F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x, ε)) ⊂ E, the image under g of the closed ball about x∈ E with radius ε . When g(x) expresses...

The Ehrlich-Aberth Method For The (2003)

Nonsymmetric Tridiagonal Eigenvalue, Dario A. Bini, Luca Gemignani, Françoise Tisseur

An algorithm based on the Ehrlich-Aberth iteration is presented for the computation of the zeros of p(#) = det(T - #I), where T is an irreducible tridiagonal matrix. The algorithm requires the...

The Ehrlich-Aberth method for the nonsymmetric tridiagonal eigenvalue problem (2003)

Dario A. Bini, Luca Gemignani, Françoise Tisseur

Abstract. An algorithm based on the Ehrlich–Aberth iteration is presented for the computation of the zeros of p(λ) = det(T −λI), where T is a real irreducible nonsymmetric tridiagonal matrix....

A chart of backward errors for singly and doubly structured eigenvalue problems (2003)

Françoise Tisseur, Pii Sx

Abstract. We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are...

The Ehrlich-Aberth Method For The (2003)

Nonsymmetric Tridiagonal Eigenvalue, Dario A. Bini, Luca Gemignani, Françoise Tisseur

An algorithm based on the Ehrlich-Aberth iteration is presented for the computation of the zeros of p(#) = det(T - #I), where T is an irreducible nonsymmetric tridiagonal matrix. The algorithm...

More on pseudospectra for polynomial eigenvalue problems and applications in control theory (2002)

Higham, Nicholas J., Tisseur, Françoise

Definitions and characterizations of pseudospectra are given for rectangular matrix poly-nomials expressed in homogeneous form: P(α,β)=α^dA_d+α^{d−1}βA_{d−1}+...+β^dA_0. It is shown that...

Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems (2002)

Higham, Nicholas J., Tisseur, Françoise, Van Dooren, Paul M.

An important class of generalized eigenvalue problems Ax=λBx is those in which A and B are Hermitian and some real linear combination of them is definite. For the quadratic eigenvalue problem (QEP)...

Simultaneous Tridiagonalization of Two Symmetric Matrices (2002)

Seamus. D. Garvey, Françoise Tisseur, Mike I. Friswell, Uwe Prells

This paper concerns pairs of symmetric matrices (K, M) and the computation of a nonsingular transformation Q that simultaneously tridiagonalizes the pair (K, M ), that is, KQ = T , Q MQ = S, (1)...

Tridiagonal-diagonal reduction of symmetric indefinite pairs. Numerical Analysis Report No (2002)

The Journal of the Society for the Foundations of Computational Mathematics Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra (2002)

Abstract. We consider the reduction of a symmetric indefinite matrix pair (A, B), with B nonsingular, to tridiagonal-diagonal form by congruence transformations. This is an important reduction in...

Jean-pierre Dedieu, Myong-hi Kim, Michael Shub, Françoise Tisseur

Abstract. Let g: E → F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x,ε)) ⊂ F, the image under g of the closed ball about x ∈ E with radius ε. When g(x)...

Tridiagonal-Diagonal Reduction (2002)

Of Symmetric Indefinite, Françoise Tisseur

We consider the reduction of a symmetric indefinite matrix pair (A, B), with B nonsingular, to tridiagonal-diagonal form by congruence transformations. This is an important reduction in solving...

Structured pseudospectra for polynomial eigenvalue problems, with applications (2001)

Tisseur, Françoise, Higham, Nicholas J.

Pseudospectra associated with the standard and generalized eigenvalue problems have been widely investigated in recent years. We extend the usual definitions in two respects, by treating the...

The quadratic eigenvalue problem (2001)

Tisseur, Françoise, Meerbergen, Karl

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the...

Stability of Structured Hamiltonian Eigensolvers (2001)

Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem (2001)

Various applications give rise to eigenvalue problems for which the matrices are Hamiltonian or skew-Hamiltonian and also symmetric or skew-symmetric. We define structured backward errors that are...

Davies, Philip I., Higham, Nicholas J., Tisseur, Françoise

A standard method for solving the symmetric definite generalized eigenvalue problem $Ax = \lambda Bx$, where $A$ is symmetric and $B$ is symmetric positive definite, is to compute a Cholesky...

Structured pseudospectra for polynomial eigenvalue problems, with applications (2001)

Françoise Tisseur, J. Higham

Abstract. Pseudospectra associated withthe standard and generalized eigenvalue problems have been widely investigated in recent years. We extend the usual definitions in two respects, by treating the...

The quadratic eigenvalue problem (2001)

Françoise Tisseur, Karl Meerbergen, Krylov Methods, Arnoldi Method, Lanczos Method

Abstract. We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both...

The Quadratic Eigenvalue Problem (2001)

Françoise Tisseur, Karl Meerbergen

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the...

Stability of Structured Hamiltonian Eigensolvers (2001)

A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra (2000)

Various applications give rise to eigenvalue problems for which the matrices are Hamiltonian or skew-Hamiltonian and also symmetric or skew-symmetric. We define structured backward errors that are...

Higham, Nicholas J., Tisseur, Françoise

The matrix 1-norm estimation algorithm used in LAPACK and various other software libraries and packages has proved to be a valuable tool. However, it has the limitations that it offers the user no...

Analysis Of The Cholesky Method With Iterative Refinement For Solving The Symmetric Definite Generalized Eigenproblem (2000)

Philip I. Davies, Nicholas J. Higham, Françoise Tisseur

. A standard method for solving the symmetric definite generalized eigenvalue problem Ax = Bx, where A is symmetric and B is symmetric positive definite, is to compute a Cholesky factorization B = LL...

Structured Pseudospectra For Polynomial Eigenvalue Problems, With Applications (2000)

Françoise Tisseur, Nicholas J. Higham

. Pseudospectra associated with the standard and generalized eigenvalue problems have been widely investigated in recent years. We extend the usual definitions in two respects, by treating the...

Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem (2000)

Philip I. Davies, Nicholas J. Higham, Françoise Tisseur

A standard method for solving the symmetric definite generalized eigenvalue problem Ax = λBx, where A is symmetric and B is symmetric positive definite, is to compute a Cholesky factorization B = LL...

A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra (2000)

Nicholas J. Higham, Françoise Tisseur

Abstract. The matrix 1-norm estimation algorithm used in LAPACK and various other software libraries and packages has proved to be a valuable tool. However, it has the limitations that it offers the...

Analysis of the Cholesky method with iterative refinement for solving the symmetric definite generalized eigenproblem, Numerical Analysis Report No (2000)

Philip I. Davies, Nicholas J. Higham, Françoise Tisseur, Mims Eprint, Philip I. Davies, Nicholas J. Higham, ...

Abstract. A standard method for solving the symmetric definite generalized eigenvalue problem Ax = λBx, where A is symmetric and B is symmetric positive definite, is to compute a Cholesky...

Newton’s method in floating point arithmetic and iterative refinement of generalized eigenvalue problems (1999)

Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems (1999)

Abstract. We examine the behavior of Newton’s method in floatingpoint arithmetic, allowing for extended precision in computation of the residual, inaccurate evaluation of the Jacobian and unstable...

Backward Error and Condition of Polynomial Eigenvalue Problems (1999)

. We examine the behaviour of Newton's method in floating point arithmetic, allowing for extended precision in computation of the residual, inaccurate evaluation of the Jacobian and unstable...

A Parallel Divide And Conquer Algorithm For The Symmetric Eigenvalue Problem On Distributed Memory Architectures (1999)

We develop normwise backward errors and condition numbers for the polynomial eigenvalue problem. The standard way of dealing with this problem is to reformulate it as a generalized eigenvalue problem...

Françoise Tisseur, Jack Dongarra

We present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a symmetric tridiagonal matrix on distributed memory architectures. The...

A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures (1999)

F Tisseur, J Dongarra, Mims Eprint, Françoise Tisseur, Jack Dongarra

Abstract. We present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a symmetric tridiagonal matrix on distributed memory architectures....

Parallelizing the Divide and Conquer Algorithm for the Symmetric Tridiagonal Eigenvalue Problem on Distributed Memory Architectures (1998)

Françoise Tisseur, J. Dongarra, Francoise Tisseur, Jack Dongarra

We present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a symmetric tridiagonal matrix on distributed memory architectures. The...

Parallelizing the Divide and Conquer Algorithm for the Symmetric Tridiagonal Eigenvalue Problem on Distributed Memory Architectures (1998)

Françoise Tisseur, Jack Dongarra, Jack Dongarra

We present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a symmetric tridiagonal matrix on distributed memory architectures. The...

Parallel Implementation of the Yau and Lu Method for Eigenvalue Computation (1997)

Parallel implementation of a symmetric eigensolver based on the Yau and Lu method (1997)

In this paper, parallel extensions of a complete symmetric eigensolver, proposed by Yau and Lu in 1993, are pre sented. First, an overview of this invariant subspace decomposition method for dense...

Domas, Stéphane, Tisseur, Françoise

In this paper, we present preliminary results on a complete eigensolver based on the Yau and Lu method. We first give an overview of this invariant subspace decomposition method for dense symmetric...

A New Deflation Criterion for the QR Algorithm (1997)

Mario Ahues, Françoise Tisseur

We present a new deflation criterion for the multishift QR algorithm motivated by convergence analysis for the basic QR algorithm. The performance of the criterion is illustrated by numerical...

Parallel Implementation of a Symmetric Eigensolver Based on the Yau and Lu Method (1997)

Stéphane Domas, Françoise Tisseur

. In this paper, we present preliminary results on a complete eigensolver based on the Yau and Lu method. We first give an overview of this invariant subspace decomposition method for dense symmetric...

Backward Stability of the QR Algorithm (1996)