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Stable factorizations of symmetric tridiagonal and triadic matrices
 SIAM J. Matrix Anal. Appl., to Appear
, 2006
"... Abstract. We call a matrix triadic if it has no more than two nonzero offdiagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider LXLT factorizations of symmetric triadic matrices, where L is unit lower triangular and X is diagonal, block diagonal ..."
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Cited by 11 (6 self)
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Abstract. We call a matrix triadic if it has no more than two nonzero offdiagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider LXLT factorizations of symmetric triadic matrices, where L is unit lower triangular and X is diagonal, block
BACKWARD ERROR ANALYSIS OF FACTORIZATION ALGORITHMS FOR SYMMETRIC AND SYMMETRIC TRIADIC MATRICES
"... We consider the LBLT factorization of a symmetric matrix where L is unit lower triangular and B is block diagonal with diagonal blocks of order 1 or 2. This is a generalization of the Cholesky factorization, and pivoting is incorporated for stability. However, the reliability of the BunchKaufman p ..."
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Cited by 2 (2 self)
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of symmetric indenite matrices by LBLT factorization incorporated with the BunchParlett pivoting strategy, generalizing results of Higham for the symmetric semidenite case. We call a matrix triadic if it has no more than two nonzero odiagonal elements in any column. A symmetric tridiagonal matrix is a
MATRIX FACTORIZATIONS, TRIADIC MATRICES, AND MODIFIED CHOLESKY FACTORIZATIONS FOR OPTIMIZATION
, 2006
"... This thesis focuses on the Choleskyrelated factorizations of symmetric matrices and their application to Newtontype optimization. A matrix is called triadic if it has at most two nonzero offdiagonal elements in each column. Tridiagonal matrices are a special case of these. We prove that the triad ..."
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Cited by 5 (3 self)
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This thesis focuses on the Choleskyrelated factorizations of symmetric matrices and their application to Newtontype optimization. A matrix is called triadic if it has at most two nonzero offdiagonal elements in each column. Tridiagonal matrices are a special case of these. We prove
Analysis of Block LDL^T Factorizations for Symmetric Indefinite Matrices
, 2007
"... We consider the block LDL^T factorizations for symmetric indefinite matrices in the form LBL^T, where L is unit lower triangular and B is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorization and its application to solving linear systems has been wells ..."
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We consider the block LDL^T factorizations for symmetric indefinite matrices in the form LBL^T, where L is unit lower triangular and B is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorization and its application to solving linear systems has been well
Modified Cholesky algorithms: A catalog with new approaches
 Math. Prog. A
"... Given an n × n symmetric possibly indefinite matrix A, a modified Cholesky algorithm computes a factorization of the positive definite matrix A+E, where E is a correction matrix. Since the factorization is often used to compute a Newtonlike downhill search direction for an optimization problem, the ..."
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Cited by 7 (1 self)
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Given an n × n symmetric possibly indefinite matrix A, a modified Cholesky algorithm computes a factorization of the positive definite matrix A+E, where E is a correction matrix. Since the factorization is often used to compute a Newtonlike downhill search direction for an optimization problem
Education
, 1991
"... • Numerical linear algebra and analysis • Numerical optimization • Machine learning and data mining ..."
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• Numerical linear algebra and analysis • Numerical optimization • Machine learning and data mining
Math. Program., Ser. A DOI 10.1007/s1010700701776 FULL LENGTH PAPER Modified Cholesky algorithms: a catalog with new
, 2006
"... Abstract Given an n × n symmetric possibly indefinite matrix A, a modified Cholesky algorithm computes a factorization of the positive definite matrix A + E, where E is a correction matrix. Since the factorization is often used to compute a Newtonlike downhill search direction for an optimization p ..."
Abstract
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Abstract Given an n × n symmetric possibly indefinite matrix A, a modified Cholesky algorithm computes a factorization of the positive definite matrix A + E, where E is a correction matrix. Since the factorization is often used to compute a Newtonlike downhill search direction for an optimization
PostPhD Employment
, 2009
"... • Parallel computing: Intel MKL for multicore threading, MPI for distributed memory systems. ..."
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• Parallel computing: Intel MKL for multicore threading, MPI for distributed memory systems.
Results 1  10
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35