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Reducing the total bandwidth of a sparse unsymmetric matrix
 SIAM Journal on Matrix Analysis and Applications
"... Abstract. For a sparse symmetric matrix, there has been much attention given to algorithms for reducing the bandwidth. As far as we can see, little has been done for the unsymmetric matrix A, which has distinct lower and upper bandwidths l and u. When Gaussian elimination with row interchanges is ap ..."
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Cited by 4 (1 self)
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Abstract. For a sparse symmetric matrix, there has been much attention given to algorithms for reducing the bandwidth. As far as we can see, little has been done for the unsymmetric matrix A, which has distinct lower and upper bandwidths l and u. When Gaussian elimination with row interchanges
Applying Schur Complements for Handling General Updates of a Large, Sparse, Unsymmetric Matrix
, 1993
"... We describe a set of procedures for computing and updating an inverse representation of a large and sparse unsymmetric matrix A. The representation is built of two matrices: an easily invertible, large and sparse matrix A0 and a dense Schur complement matrix S. An e cient heuristic is given that nds ..."
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We describe a set of procedures for computing and updating an inverse representation of a large and sparse unsymmetric matrix A. The representation is built of two matrices: an easily invertible, large and sparse matrix A0 and a dense Schur complement matrix S. An e cient heuristic is given
A REFINED UNSYMMETRIC LANCZOS EIGENSOLVER FOR COMPUTING ACCURATE EIGENTRIPLETS OF A REAL UNSYMMETRIC MATRIX∗
"... Dedicated to Gene Golub on the occasion of his 75th birthday Abstract. For most unsymmetric matrices it is difficult to compute many accurate eigenvalues using the primitive form of the unsymmetric Lanczos algorithm (ULA). In this paper we propose a modification of the ULA. It is related to ideas u ..."
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Cited by 1 (0 self)
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Dedicated to Gene Golub on the occasion of his 75th birthday Abstract. For most unsymmetric matrices it is difficult to compute many accurate eigenvalues using the primitive form of the unsymmetric Lanczos algorithm (ULA). In this paper we propose a modification of the ULA. It is related to ideas
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2 The Effects of Unsymmetric Matrix Permutations and Scalings in Semiconductor Device and Circuit Simulation
"... Abstract — The solution of large sparse unsymmetric linear systems is a critical and challenging component of semiconductor device and circuit simulations. The time for a simulation is often dominated by this part. The sparse solver is expected to balance different, and often conflicting requirement ..."
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Abstract — The solution of large sparse unsymmetric linear systems is a critical and challenging component of semiconductor device and circuit simulations. The time for a simulation is often dominated by this part. The sparse solver is expected to balance different, and often conflicting
Solving unsymmetric sparse systems of linear equations with PARDISO
 Journal of Future Generation Computer Systems
, 2004
"... Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to ..."
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Cited by 195 (11 self)
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to extend these concepts further and unsymmetric prepermutation of rows is used to place large matrix entries on the diagonal. Complete block diagonal supernode pivoting allows dynamical interchanges of columns and rows during the factorization process. The level3 BLAS efficiency is retained
An Unsymmetrized Multifrontal LU Factorization
 SIAM Journal on Matrix Analysis and Applications
, 2000
"... A well known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A+A T and use it as a computational graph to drive the numerical factorization. This approach, although very efficient on a lar ..."
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Cited by 24 (4 self)
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A well known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A+A T and use it as a computational graph to drive the numerical factorization. This approach, although very efficient on a
SPARSKIT: a basic tool kit for sparse matrix computations  Version 2
, 1994
"... . This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boei ..."
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Cited by 317 (22 self)
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. This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell
An UnsymmetricPattern Multifrontal Method for Sparse LU Factorization
 SIAM J. MATRIX ANAL. APPL
, 1994
"... Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallelvector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops ..."
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Cited by 150 (27 self)
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loops by using dense matrix kernels. However, no efficient LU factorization algorithm based primarily on dense matrix kernels exists for matrices whose pattern is very unsymmetric. We address this deficiency and present a new unsymmetricpattern multifrontal method based on dense matrix kernels
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