Extensions of Certain Graph-based Algorithms for Preconditioning (2009)
David Fritzsche, Andreas Frommer, Daniel B. Szyld, Ax B
We want to solve the linear system
This routine solves a real sparse nonsymmetric system of linear equations: (2009)
Ax B, Cgs (see Sonneveld, Or Bi-cgstab
f11dec nag sparse nsym sol (f11dec) 1. Purpose nag sparse nsym sol (f11dec) solves a real sparse nonsymmetric system of linear equations, represented in coordinate storage format, using a restarted...
Preconditioning sparse nonsymmetric linear systems with the Sherman-Morrison formula (2008)
R. Bru, J. Cerd Án, J. Mar Ín, J. Mas, Ax B
Abstract. Let Ax = b be a large, sparse, nonsymmetricsystem of linear equations. A new sparse approximate inverse preconditioning technique for such a class of systems is proposed. We show how the...
Abstract. The purpose of this work is to introduce the main aspects of conjugate direction methods for solving systems of linear algebraic equations. We emphasize the algorithms and their analysis...
Amir Beck, Amir Beck P, D. Sima, S. Van Huffel, Amir Beck P, Amir Beck P, ...
A fixed- LS s.t. min w,x �w�2 Ax = b + w minimal perturbation to rhs which makes this linear system consistent Ax ≈ b
• Primal Conic optimization (2008)
Kartik Krishnan, John Mitchell (rpi, Semidefinite Optimization, Ax B
conic programming
Randolph E. Bank, C. Douglas, Ax B
Abstract. Weinvestigatemethods for e ciently implementing a class of incomplete factorization
A Bibliography of ACM Transactions on Mathematical Software Title word cross-reference (2008)
h →∞[443]. i [103]. I0 [148].
2.1 Solving Linear Systems (2008)
One of the problems encountered most frequently in scientific computation is the solution of systems of simultaneous linear equations. This chapter covers the solution of linear systems by Gaussian...
. PROPERTIES OF THE SOLVER 1.1. Operating Requirements (2007)
52> n in the range of 100,000--200,000 for computers having 512MB--4GB of memory. (3) Provides close to peak performance across all vector and vector/parallel (computer architectures having few...
An Efficient Implementation for SSOR and Incomplete Factorization Preconditionings (2007)
Randolph E. Bank, Craig C. Douglas, C. Douglas, Ax B
. We investigate methods for efficiently implementinga class of incomplete factorization preconditioners which includes Symmetric Gauss Seidel [9], SSOR [9], generalized SSOR [1], Dupont Kendall...
An Efficient Implementation For Ssor And Incomplete Factorization Preconditionings (2007)
Randolph Bank Craig, C. Douglas, Ax B
. We investigate methods for efficiently implementing a class of incomplete factorization preconditioners which includes Symmetric Gauss Seidel [9], SSOR [9], generalized SSOR [1], Dupont Kendall...
A Comparison of Pivoting Strategies for the Direct LU Factorization (2007)
We combine the idea of the direct LU factorization with the idea of the pivoting strategy in the usual Gaussian elimination and show that two so-called total scaled and total pivoting strategies can...
Improved Black Box Multigrid For Definite And Indefinite Problems (2007)
. A two-level analysis method for certain separable problems is introduced. Unlike standard twolevel analysis methods, based on Fourier analysis, it is based on spectral analysis, hence applicable to...
. PROPERTIES OF THE SOLVER 1.1. Operating Requirements (2007)
I/O activities. LRA CDENSE defines large complex dense coefficient matrices as n in the range of 20,000--50,000 for computers having 256MB--512MB of memory and n in the range of 70,000--150,000 for...
C. Brezinski, M. Redivo Zaglia, H. Sadok, Ax B
A breakdown (due to a division by zero) can arise in the algorithms for implementing Lanczos' method because of the non--existence of some formal orthogonal polynomials or because the recurrence...
L-CURVE CURVATURE BOUNDS (2007)
Via Lanczos Bidiagonalization, D. Calvetti, P. C. Hansen, L. Reichel, Ax B
Abstract. The L-curve is often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side contaminated by...
Spectral factorization Examples (2007)
Shao-po Wu, Stephen Boyd (stanford, Ax B
FIR filters & magnitude specs
Peter Arbenz, Ax B, P. Arbenz, P. Arbenz, P. Arbenz
Solve in parallel and in a stable way
EFFICIENT COMPUTATION OF STATISTICS FOR BANDED MULTIVARIATE NORMAL DISTRIBUTIONS (2007)
Abstract. We look at the problem of computing statistics for a large multivariate normal distribution whose precision matrix has limited bandwidth. In particular, we wish to randomly sample from the...
Alberto Caprara, Matteo Fischetti, Ax B
Given the integer polyhedron P I: = convfx 2 Z n: Ax bg, where A 2 Z m\Thetan and b 2 Z m
A comparison of deflation and the balancing preconditioner (2006)
Abstract. In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare the well-known balancing preconditioner used in domain...
• Conclusions and future work 1 • Primal • Dual • Facts: Conic optimization (2004)
Kartik Krishnan, Tamás Terlaky (mac, Ax B
second order cone programming
A Bluffers ’ Guide to Iterative Methods for Systems of Linear Equations (2003)
Iterative methods are a popular way of solving linear systems of equation
Block descent methods and hybrid procedures for linear systems, Numerical Algorithms 29 (2002)
This paper is dedicated to the memory of Ruediger Weiss In this paper, we dene and study several types of block descent methods for the simultaneous solution of a system of linear equations with...
On the separation of maximally violated mod-k cuts (2000)
Alberto Caprara, Matteo Fischetti, Adam N. Letchford, Ax B
Separation is of fundamental importance in cutting-plane based techniques for Integer Linear Programming (ILP). In recent decades, a considerable research eort has been devoted to the denition of...
Structured Backward Error and Condition Number for Linear Systems of the Type A*Ax = b (2000)
Ax B, Valérie Frayssé, Serge Gratton, Vincent Toumazou
We present a formulation for the structured condition number and for the structured backward error for the linear system A Ax = b, when the rectangular matrix A is subjected to normwise...
Gmres-Type Methods For Inconsistent Systems (2000)
Calvetti Lewis And, D. Calvetti, B. Lewis, L. Reichel, Ax B
The behavior of iterative methods of GMRES-type when applied to singular, possibly inconsistent, linear systems is discussed and conditions under which these methods converge to the least-squares...
The Conjugate Gradient Method (1999)
Martin H. Gutknecht, Ax B, Ax B, Ax X
banded matrix, the less eective they are due to ll-in. If original physical problem is 2- or 3-dimensional, A is far from being narrowly banded. c Martin H. Gutknecht, September 2, 1999 2 Fixed point...
On a structured backward error analysis for linear systems of the type A*Ax = b (1998)
Ax B, Valérie Frayssé, Serge Gratton, Vincent Toumazou
The authors present a formulation for the structured condition number and bounds for the structured backward error for the linear system A Ax = b when the square matrix A is subjected to normwise...
The Conjugate Gradient Method (1998)
Martin H. Gutknecht, Ax B, Ax B, Ax X
are due to fill-in. If original physical problem is 2- or 3-dimensional, A is far from being narrowly banded. c flMartin H. Gutknecht, November 16, 1998 Fixed point iteration A mathematician's...
Estimation of the L-Curve via Lanczos Bidiagonalization (1997)
D. Calvetti, G. H. Golub, L. Reichel, Ax B
The L-curve criterion is often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side contaminated by...
Note on the backward error analysis of linear systems of the kind A*Ax = b (1996)
Valérie Fraysse, Ax B, Serge Gratton, Vincent Toumazou
The authors derive a formulation for the structured condition number and bounds for structured backward error for the linear system A Ax = b when the square matrix A is subject to normwise...
Scalable Parallel Preconditioning With The Sparse Approximate Inverse Of Triangular Matrices (1996)
. In this paper an approach is proposed for preconditioning large general sparse matrices. This approach combines the scalability of explicit preconditioners with the preconditioning efficiency of...
A New Matrix Decomposition For Signal Processing (1994)
Franklin Luk, Sanzheng Qiao, Ax B
. To solve the noise subspace problem, we extend the generalized singular value decomposition to a new decomposition that can be updated at a low cost. In addition, we show how a forgetting factor...
Ordering, Anisotropy, And Factored Sparse Approximate Inverses
. We consider ordering techniques to improve the performance of factored sparse approximate inverse preconditioners, concentrating on the AINV technique of M. Benzi and M. Tuma. Several practical...