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171
On Hamiltonian and Symplectic Lanczos Processes
 Linear Algebra Appl
, 2002
"... Large sparse Hamiltonian eigenvalue problems arise in a variety of contexts. These problems can be attacked directly, or they can rst be transformed to problems having some related structure, such as symplectic or skew Hamiltonian. In the interest of eciency, stability, and accuracy, such probl ..."
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Cited by 13 (2 self)
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Large sparse Hamiltonian eigenvalue problems arise in a variety of contexts. These problems can be attacked directly, or they can rst be transformed to problems having some related structure, such as symplectic or skew Hamiltonian. In the interest of eciency, stability, and accuracy, such problems should be solved by methods that preserve the structure, whether it be Hamiltonian, skew Hamiltonian, or symplectic.
ON THE LONGTERM BEHAVIOR OF THE LANCZOS PROCESS
"... Abstract. We investigate the longterm behavior of the classical Lanczos process in an attempt to pave the way to an ecient and robust eigensolver that can nd all the eigenvalues of large sparse symmetric matrices. We are interested in the convergence of classical Lanczos (i.e., without reorthogona ..."
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Abstract. We investigate the longterm behavior of the classical Lanczos process in an attempt to pave the way to an ecient and robust eigensolver that can nd all the eigenvalues of large sparse symmetric matrices. We are interested in the convergence of classical Lanczos (i.e., without re
Error Estimation Of The Pad E Approximation Of Transfer Functions Via The Lanczos Process
, 1997
"... . Krylov subspace based moment matching algorithms, such as PVL (Pade approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matrix point ..."
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Cited by 1 (0 self)
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. Krylov subspace based moment matching algorithms, such as PVL (Pade approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matrix
The Improved Unsymmetric Lanczos Process on Massively Distributed Memory Computers
 4th International Symposium on Solving Irregularly Structured Problems in Parallel (IRREGULAR97
, 1997
"... For the eigenvalues of a large and sparse unsymmetric coefficient matrix, we propose an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. Stability is obtained by a coupled twoterm recurrences procedure that generates Lanczo ..."
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Cited by 1 (1 self)
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For the eigenvalues of a large and sparse unsymmetric coefficient matrix, we propose an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. Stability is obtained by a coupled twoterm recurrences procedure that generates
Efficient Implementation of the Improved Unsymmetric Lanczos Process on Massively Distributed Memory Computers
"... . For the eigenvalues of a large and sparse unsymmetric coefficient matrix, we have proposed an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. The algorithm is derived such that all inner products and matrixvector multipl ..."
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. For the eigenvalues of a large and sparse unsymmetric coefficient matrix, we have proposed an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. The algorithm is derived such that all inner products and matrix
A QRdecomposition of block tridiagonal matrices generated by the block Lanczos process
"... ... to compute a QR decomposition of a tridiagonal coefficient matrix gained in the Lanczos process. This QR decomposition is constructed by an update scheme applying in every step a single Givens rotation. Using complex Householder reflections we generalize this idea to block tridiagonal matrices t ..."
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Cited by 1 (1 self)
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... to compute a QR decomposition of a tridiagonal coefficient matrix gained in the Lanczos process. This QR decomposition is constructed by an update scheme applying in every step a single Givens rotation. Using complex Householder reflections we generalize this idea to block tridiagonal matrices
Error estimation of the Pad'e approximation of transfer functions via the Lanczos process
 Trans. Numer. Anal
, 1998
"... Abstract. Krylov subspace based moment matching algorithms, such as PVL (Padé approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matr ..."
Abstract

Cited by 28 (8 self)
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Abstract. Krylov subspace based moment matching algorithms, such as PVL (Padé approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from
Stable and Passive ReducedOrder Models Based on Partial Padé Approximation Via the Lanczos Process
 Numerical Analysis Manuscript No. 97310, Bell Laboratories
, 1997
"... This paper describes the use of partial Padé approximation to generate stable and passive reducedorder models of linear circuits. For similarlysized models, partial Padébased reducedoreder modeling has superior momentmatching capabilities than competing techniques based on the Arnoldi process. ..."
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Cited by 11 (3 self)
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. The paper introduces PVLß, an algorithm for computing partial Padébased reducedorder models via the Lanczos process. The effectiveness of this modeling methodology is illustrated by numerical examples.
A symmetric band Lanczos process based on coupled recurrences and some applications. Numerical Analysis Manuscript 00804, Bell Laboratories
, 2000
"... Abstract. The symmetric band Lanczos process is an extension of the classical Lanczos algorithm for symmetric matrices and single starting vectors to multiple starting vectors. After n iterations, the symmetric band Lanczos process has generated an n × n projection, Ts n, of the given symmetric matr ..."
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Cited by 7 (3 self)
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Abstract. The symmetric band Lanczos process is an extension of the classical Lanczos algorithm for symmetric matrices and single starting vectors to multiple starting vectors. After n iterations, the symmetric band Lanczos process has generated an n × n projection, Ts n, of the given symmetric
Results 1  10
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171