Analysis of Damped Mass-Spring Systems for Sound Synthesis (2009)
There are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected...
Analysis of Damped Mass-Spring Systems for Sound Synthesis (2009)
There are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected...
Condition Numbers for the Scaled Total Least Squares Problems ∗ (2008)
Liangmin Zhou, Lijing Lin, Yimin Wei, Sanzheng Qiao
The standard approaches to solving an overdetermined linear system Bx ≈ c construct minimal corrections to the vector c and/or the matrix B such that the corrected system is consistent, such as the...
A Twisted Factorization Method for Symmetric SVD of a Complex Symmetric Tridiagonal Matrix (2008)
This paper presents an O(n 2) method based on twisted factorization for computing the Takagi vectors of an n-by-n complex symmetric tridiagonal matrix with known singular values. Since the singular...
Wei Xu, Sanzheng Qiao, Yimin Wei
algorithm for solving rank-deficient scaled total least square problems
A Twisted Factorization Method for Symmetric SVD of a Complex Symmetric Tridiagonal Matrix (2008)
This paper presents an O(n 2) method based on twisted factorization for computing the Takagi vectors of an n-by-n complex symmetric tridiagonal matrix with known singular values. Since the singular...
A High Performance C Package for Tridiagonalization of Complex Symmetric Matrices (2008)
Block algorithms have better performance than scalar and single vector algorithms due to their exploitation of memory hierarchy. This paper presents a high performance C implementation of a block...
A Lanczos Bidiagonalization Algorithm for Hankel Matrices ∗ (2008)
Kevin Browne, Sanzheng Qiao, Yimin Wei
This paper presents an O(mn log m) algorithm for bidiagonalizing a Hankel matrix. An m×n Hankel matrix is reduced to a real bidiagonal matrix in O((m+n)n log(m+n)) floating-point operations (flops)...
A High Performance C Package for Tridiagonalization of Complex Symmetric Matrices (2008)
Block algorithms have better performance than scalar and single vector algorithms due to their exploitation of memory hierarchy. This paper presents a high performance C implementation of a block...
Inspection Procedures for Critical Programs that Model Physical Phenomena (2008)
Konstantin Kreyman, David Lorge Parnas, Sanzheng Qiao
This paper addresses the problem of assuring the accuracy and trustworthiness of computer programs that are based on models of physical phenomena. It begins by explaining why such programs can be...
Automatically Testing Numerical Stability (2007)
this report, we present an automatic method for testing numerical stability. It automatically selects a set of input data that will reveal possible instability of the numerical software under testing.
Weiwei Gao Computing, Weiwei Gao, Sanzheng Qiao
This paper describes a parallel implementation of a sequence alignment algorithm for biomolecular sequence analysis. It uses multiple threaded programming for the most time consuming functions and...
Global Meeting Plus (GMP) (2007)
Dan Yan, Polina Galkin, Sanzheng Qiao
Global Meeting Plus (GMP) is a Web-based collaborative GroupWare application, which consists of chat-channel, whiteboard, database, communication security, and pillow-talking. The chat-channel is for...
Approximating the PSVD and QSVD (2007)
. This paper presents an adaptive method for approximating the SVD of the product AB or the quotient AB \Gamma1 of two matrices A and B. Specifically, it computes an approximation of the complete...
Decaying Exponentials and Signal Decomposition (2007)
Franklin T. Luk, Sanzheng Qiao
this paper, we first show an association between the problem of finding r
Prediction Error Computation on a Grid (2007)
Wallace E. Larimore, Franklin T. Luk, Sanzheng Qiao
This paper presents a distributed algorithm for prediction error computation. 1
Inspection Procedures for Critical Programs that Model Physical Phenomena (2007)
Konstantin Kreyman, David Lorge Parnas, Sanzheng Qiao
This paper addresses the problem of assuring the accuracy and trustworthiness of computer programs that are based on models of physical phenomena. It begins by explaining why such programs can be...
Huaian Diao, Yimin Wei, Sanzheng Qiao
In this paper, we study the displacement rank of the Drazin inverse. Both Sylvester displacement and the generalized displacement are discussed. We present upper bounds for the ranks of the...
In this paper, we present a novel approach to the problem of exponential decomposition. This method can compute the knots in O(n 2) oating-point operations and O(n) storage, where n is the length of...
Parallel Implementation of a Validated Method for Initial Value Problems (2007)
Abstract Validated (interval) method is used to solve the initial value problems (IVPs) of ordinary dierential equations (ODEs). Compare to traditional methods, validated method can provide a...
Unifying unitary and hyperbolic transformations (2007)
Adam Bojanczyk, Sanzheng Qiao, Allan O. Steinhardt
In this paper we describe unified formulas for unitary and hyperbolic reflections and rotations, and show how these unified transformations can be used to compute a Hermitian triangular decomposition...
We present a unied representation theorem for the Drazin inverse of linear operators in Hilbert space and a general error bound. Five specic expressions, computational procedures, and their error...
Franklin T. Luk, Sanzheng Qiao
We present an O(n 2 log n) algorithm for nding all the singular values of an n-by-n complex Hankel matrix.
An Analysis of Rank-Deficient Scaled Total Least Squares Problem (2007)
Wei Xu, Yimin Wei, Sanzheng Qiao
In this paper, we study the scaled total least squares problems of rank-deficient linear systems. We present a solution for rank-deficient scaled total least squares and discuss the relation between...
Solving Constrained Matrix Equations and Cramer Rule (2007)
Guorong Wang Sanzheng, Cramer Rule, Guorong Wang, Sanzheng Qiao
This paper presents the solution of a general constrained matrix equation using generalized inverses and gives an explicit expression for the elements of the solution matrix using Cramer rule.
A Parallel Jacobi Method for the Takagi Factorization (2007)
In this paper, we discuss a special form of the singular value decomposition (SVD), called Takagi factorization, of a complex-symmetric matrix. We present a multthreading parallel Jacobi algorithm...
Contemporary Mathematics a Fast Singular Value Algorithm for Hankel Matrices (2007)
Franklin T. Luk, Sanzheng Qiao
We present an O(n 2 values of an n-by-n complex Hankel matrix. We take advantage of complex symmetry and the Hankel structure. Our method is based on a modi ed Lanczos process and the Fast Fourier...
Condition Number for Weighted Linear Least Squares Problem and Its Condition Number (2007)
Yimin Wei, Huaian Diao, Sanzheng Qiao
In this paper, we investigate the condition numbers for the generalized matrix inversion and the rank de cient linear least squares problem: min x kAx bk 2 , where A is an m-by-n (m n) rank de cient...
Block Lanczos tridiagonalization of complex symmetric matrices (2005)
We present two orthogonalization schemes for stablizing Lanczos tridiagonalization of a complex symmetric matrix.
A divide-and-conquer method for the Takagi factorization (2005)
Abstract. This paper presents a divide-and-conquer method for computing the symmetric singular value decomposition, or Takagi factorization, of a complex symmetric and tridiagonal matrix. An analysis...
Block Lanczos tridiagonalization of complex symmetric matrices (2005)
Sanzheng Qiao, Guohong Liu, Wei Xu
The classic Lanczos method is an effective method for tridiagonalizing real symmetric matrices. Its block algorithm can significantly improve performance by exploiting memory hierarchies. In this...
A divide-and-conquer method for the Takagi factorization (2005)
This paper presents a divide-and-conquer method for computing the Takagi factorization, or symmetric singular value decomposition, of a complex symmetric and tridiagonal matrix. An analysis of...
Block Lanczos tridiagonalization of complex symmetric matrices (2005)
Sanzheng Qiao, Guohong Liu, Wei Xu
The classic Lanczos method is an effective method for tridiagonalizing real symmetric matrices. Its block algorithm can significantly improve performance by exploiting memory hierarchies. In this...
Displacement Rank of the Drazin Inverse (2004)
Huaian Diao, Yimin Wei, Sanzheng Qiao, Toeplitz Matrix
In this paper, we study thedisplacemBB rank of the Drazin inverse. Both Sylvesterdisplacem3x and the generalized displacemdv are discussed. We present upper bounds for the ranks of thedisplacemBIT of...
Condition Numbers for Structured Least Squares (2003)
Wei Xu, Yimin Wei, Sanzheng Qiao
This paper studies the normwise perturbation theory for structured least squares problems. The structures under investigation are symmetric, persymmetric, skewsymmetric, Toeplitz and Hankel. We...
Computing the singular values of 2-by-2 complex matrices (2002)
This paper describes an algorithm for the singular value decomposition of a 2-by-2 complex matrix. It computes accurate singular values.
Computing the Singular Values of 2-by-2 Complex Matrices (2002)
Sanzheng Qiao And, Sanzheng Qiao, Xiaohong Wang
This paper describes an algorithm for the singular value decomposition of a 2-by-2 complex matrix. It computes accurate singular values. Keywords Singular value decomposition (SVD), Jacobi method. 1
Unifying Unitary and Hyperbolic Transformations (2000)
Adam Bojanczyk, Sanzheng Qiao, Allan O. Steinhardt
In this paper we describe uni ed formulas for unitary and hyperbolic reflections and rotations, and show how these unified transformations can be used to compute a Hermitian triangular decomposition...
Analysis of a Fast Hankel Eigenvalue Algorithm (1999)
Franklin T. Luk, Sanzheng Qiao
This paper analyzes the important steps of an O(n 2 log n) algorithm for finding the eigenvalues of a complex Hankel matrix. The three key steps are a Lanczos-type tridiagonalization algorithm, a...
An Automatic Logfile Analyzer for Parallel Programs (1999)
The Logfile Analyzer is a tool for automatically analyzing the logfiles generated during a parallel program execution. The purpose of the tool is to check the communication consistency of parallel...
Analysis of a Fast Eigenvalue Algorithm for Hankel Matrices (1999)
This paper analyzes a recently proposed fast algorithm for finding the eigenvalues of a complex Hankel matrix. The key step is an O(n² log 2 n) Lanczos-type algorithm that tridiagonalizes...
Analysis of the Unified Transformations (1999)
We show the singular values of the unified transformations [6], propose pivoting strategies for downdating, and present a stability analysis. Keywords: Hyperbolic transformations, downdating,...
Analysis of a Linearly Constrained Least Squares Algorithm for Adaptive Beamforming. (1998)
Luk, Franklin T., Qiao, Sanzheng
The problem of linearly constrained least squares has many applications in signal processing. In this paper, we present a perturbation analysis of a linearly constrained least squares algorithm for...
Analysis of a Linearly Constrained Least Squares Algorithm for Adaptive Beamforming. (1998)
Luk, Franklin T., Qiao, Sanzheng
The problem of linearly constrained least squares has many applications in signal processing. In this paper, we present a perturbation analysis of a linearly constrained least squares algorithm for...
A fast eigenvalue algorithm for Hankel matrices (1998)
Franklin T. Luk, Sanzheng Qiao
We present an algorithm that can nd all the eigenvalues of an nn complex Hankel matrix in O(n 2 log n) operations. Our scheme consists of an O(n 2 log n) Lanczos-type tridiagonalization procedure and...
A Fast Eigenvalue Algorithm for Hankel Matrices (1998)
Franklin T. Luk, Sanzheng Qiao
We present an algorithm that can nd all the eigenvalues of an nn complex Hankel matrix in O(n 2 log n) operations. Our scheme consists of an O(n 2 log n) Lanczos-type tridiagonalization procedure and...
A Robust and Efficient Algorithm for Evaluating Erlang B Formula (1998)
this paper, we first introduce the formula involved in the Erlang B traffic model. We then analyze the formula for numerical evaluation. Finally, we present a robust and efficient algorithm for...
A Fast Eigenvalue Algorithm for Hankel Matrices (1998)
Franklin T. Luk, Sanzheng Qiao
We present an O(n 2 log n) algorithm for finding all the eigenvalues of an n \Theta n complex Hankel matrix. Keywords: Hankel matrix, Toeplitz matrix, circulant matrix, fast Fourier transform,...
Unifying Unitary and Hyperbolic Rotations and Reflectors (1998)
In Cholesky updating, Givens rotations or Householder transformations are used. In Cholesky downdating, where the matrix resulted from downdating is positive definite, hyperbolic rotations or...
Regularized Iterative Blind Deconvolution using Recursive Inverse Filtering (1997)
Michael K. Ng, Robert J. Plemmons, Sanzheng Qiao
Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Blind restoration is the...
Regularized Blind Deconvolution using Recursive Inverse Filtering (1997)
Michael K. Ng, Robert J. Plemmons, Sanzheng Qiao
. Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Blind restoration is the...
Using Complex-Orthogonal Transformations to Diagonalize a Complex Symmetric Matrix (1997)
Franklin T. Luk, Sanzheng Qiao
In this paper, we propose the use of complex-orthogonal transformations for finding the eigenvalues of a complex symmetric matrix. Using these special transformations can significantly reduce...
A Matrix Representation of Phylogenetic Trees (1997)
. In this paper we begin by describing two currently used methods for evaluating phylogenetic trees, one proposed by Fitch and Margoliash [5] and the other proposed by Saitou and Nei [7]. Both...
An Adaptive Algorithm for Interference Cancelling in Array Processing (1996)
In array processing, one technique for cancelling interference in the presence of colored noise is the ULLV decomposition of a pair of matrices. The factorization is stable and accurate, and is easy...
A Symmetric Rank-Revealing Toeplitz Matrix Decomposition (1996)
Franklin T. Luk, Sanzheng Qiao
. In signal and image processing, regularization often requires a rank-revealing decomposition of a symmetric Toeplitz matrix with a small rank deficiency. In this paper, we present an efficient...
A Rank-Revealing Decomposition of Symmetric Toeplitz Matrices (1995)
Franklin T. Luk, Sanzheng Qiao
In signal and image processing, regularization often requires a rank-revealing decomposition of a symmetric Toeplitz matrix with a small rank deficiency. In this paper, we present an efficient...
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...
Regularization of RIF Blind Image Deconvolution
Michael Ng Robert, Robert J. Plemmons, Sanzheng Qiao
Blind restoration is the process of estimating both the true image and the blur from the degraded image, using only partial information about degradation sources and the imaging system. Our main...