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2,441
Accurate Singular Values of Bidiagonal Matrices
 SIAM J. SCI. STAT. COMPUT
, 1990
"... Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magni ..."
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Cited by 128 (18 self)
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Computing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich computes all the singular values of a bidiagonal matrix to high relative accuracy independent
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 645 (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
Lanczos Bidiagonalization With Partial Reorthogonalization
, 1998
"... A partial reorthogonalization procedure (BPRO) for maintaining semiorthogonality among the left and right Lanczos vectors in the Lanczos bidiagonalization (LBD) is presented. The resulting algorithm is mathematically equivalent to the symmetric Lanczos algorithm with partial reorthogonalization (PR ..."
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Cited by 83 (0 self)
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(PRO) developed by Simon, but works directly on the Lanczos bidiagonalization of A. For computing the singular values and vectors of a large sparse matrix with high accuracy, the BPRO algorithm uses only half the amount of storage and a factor of 34 less work compared to methods based on PRO applied
Accurately Counting Singular Values of Bidiagonal Matrices
 SIAM J. Matrix Anal. Appl
, 1998
"... We have developed algorithms to count singular values of a bidiagonal matrix which are greater than a specified value. This requires the transformation of the singular value problem to an equivalent symmetric eigenvalue problem. The counting of singular values is paramount in the design of bisection ..."
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Cited by 6 (0 self)
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We have developed algorithms to count singular values of a bidiagonal matrix which are greater than a specified value. This requires the transformation of the singular value problem to an equivalent symmetric eigenvalue problem. The counting of singular values is paramount in the design
A Lanczos Bidiagonalization Algorithm for Hankel Matrices ∗
"... 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)) floatingpoint operations (flops) using the Lanczos method with modified partial orthogonalization and restart schemes to improve its st ..."
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Cited by 4 (2 self)
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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)) floatingpoint operations (flops) using the Lanczos method with modified partial orthogonalization and restart schemes to improve its
A differential equation approach to the singular value decomposition of bidiagonal matrices
 Linear Algebra and Its Applications
, 1986
"... We consider the problem of approximating the singular value decomposition of a bidiagonal matrix by a oneparameter family of differentiable matrix flows. It is shown that this approach can be fully expressed as an autonomous, homogeneous, and cubic dynamical system. Asymptotic behavior is justified ..."
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Cited by 5 (1 self)
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We consider the problem of approximating the singular value decomposition of a bidiagonal matrix by a oneparameter family of differentiable matrix flows. It is shown that this approach can be fully expressed as an autonomous, homogeneous, and cubic dynamical system. Asymptotic behavior
The bidiagonal singular values decomposition and Hamiltonian mechanics
 SIAM J. Num. Anal
, 1991
"... We consider computing the singular value decomposition of a bidiagonal matrixB. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative accu ..."
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Cited by 29 (6 self)
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We consider computing the singular value decomposition of a bidiagonal matrixB. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative
Towards a Fast and Robust O(n²) Algorithm for the Bidiagonal SVD
"... We describe a new algorithm for computing the singular value decomposition of a real bidiagonal matrix, which uses ideas developed by Großer and Lang that extend the MRRR algorithm by Dhillon and Parlett for the tridiagonal symmetric eigenproblem. This new algorithm inherits all the favorable prope ..."
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We describe a new algorithm for computing the singular value decomposition of a real bidiagonal matrix, which uses ideas developed by Großer and Lang that extend the MRRR algorithm by Dhillon and Parlett for the tridiagonal symmetric eigenproblem. This new algorithm inherits all the favorable
Accurately Counting Singular Values of Bidiagonal Matrices
"... Wehave developed algorithms to count singular values of a bidiagonal matrix which are greater than a speci ed value. This requires the transformation of the singular value problem to an equivalent symmetric eigenvalue problem. The counting of singular values is paramount in the design of bisection a ..."
Abstract
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Wehave developed algorithms to count singular values of a bidiagonal matrix which are greater than a speci ed value. This requires the transformation of the singular value problem to an equivalent symmetric eigenvalue problem. The counting of singular values is paramount in the design of bisection
Parallel Computation Of Spectral Portraits Of Matrices By Bidiagonalization
, 1995
"... : We describe parallel programs for computation of spectral portraits of matrices on Paragon and Connection Machine 5. The method used consists of bidiagonal reduction of a complex square matrix by unitary Householder transformations and computation of the minimal singular value of the resulting rea ..."
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: We describe parallel programs for computation of spectral portraits of matrices on Paragon and Connection Machine 5. The method used consists of bidiagonal reduction of a complex square matrix by unitary Householder transformations and computation of the minimal singular value of the resulting
Results 1  10
of
2,441