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Fast solver for Toeplitz bidiagonal systems of linear equations
"... We present a new efficient parallel algorithm for solving the first order linear recurrence systems with constant coefficients which is equivalent to the problem of solving Toeplitz bidiagonal systems of linear equations. The algorithm is formulated in the terms of level 1 and 2 BLAS (Basic Linear A ..."
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We present a new efficient parallel algorithm for solving the first order linear recurrence systems with constant coefficients which is equivalent to the problem of solving Toeplitz bidiagonal systems of linear equations. The algorithm is formulated in the terms of level 1 and 2 BLAS (Basic Linear
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 82 (0 self)
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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
A New Efficient Algorithm for Computing Gröbner Bases (F4)
 IN: ISSAC ’02: PROCEEDINGS OF THE 2002 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION
, 2002
"... This paper introduces a new efficient algorithm for computing Gröbner bases. To avoid as much as possible intermediate computation, the algorithm computes successive truncated Gröbner bases and it replaces the classical polynomial reduction found in the Buchberger algorithm by the simultaneous reduc ..."
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Cited by 366 (57 self)
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reduction of several polynomials. This powerful reduction mechanism is achieved by means of a symbolic precomputation and by extensive use of sparse linear algebra methods. Current techniques in linear algebra used in Computer Algebra are reviewed together with other methods coming from the numerical field
Conjugate Gradient Methods for Toeplitz Systems
 SIAM Review
, 1996
"... In this expository paper, we survey some of the latest developments on using preconditioned conjugate gradient methods for solving Toeplitz systems. One of the main results is that the complexity of solving a large class of nbyn Toeplitz systems is reduced to O(n log n) operations as compared to O ..."
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Cited by 174 (40 self)
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to O(n log 2 n) operations required by fast direct Toeplitz solvers. Different preconditioners proposed for Toeplitz systems are reviewed. Applications to Toeplitzrelated systems arising from partial differential equations, queueing networks, signal and image processing, integral equations, and time
Regularization tools – a matlab package for analysis and solution of discrete illposed problems
 Numerical Algorithms
, 1994
"... The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents ..."
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Cited by 276 (8 self)
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The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents
A Lanczos bidiagonalization algorithm for Hankel
, 2007
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy Available online at www.sciencedirect.com
Spectra, Pseudospectra, and Localization for Random Bidiagonal Matrices
 Comm. Pure Appl. Math
"... There has been much recent interest, initiated by work of the physicists Hatano and Nelson, in the eigenvalues of certain random nonhermitian periodic tridiagonal matrices and their bidiagonal limits. These eigenvalues cluster along a \bubble with wings" in the complex plane, and the correspon ..."
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Cited by 16 (4 self)
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that characterize the spectra, pseudospectra, and numerical range for the four cases of nite bidiagonal matrices, in nite bidiagonal matrices (\stochastic Toeplitz operators"), nite periodic matrices, and doubly in nite bidiagonal matrices (\stochastic Laurent operators").
Restarted block Lanczos bidiagonalization methods, Numer. Algorithms
"... Abstract. The problem of computing a few of the largest or smallest singular values and associated singular vectors of a large matrix arises in many applications. This paper describes restarted block Lanczos bidiagonalization methods based on augmentation of Ritz vectors or harmonic Ritz vectors by ..."
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Cited by 19 (6 self)
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Abstract. The problem of computing a few of the largest or smallest singular values and associated singular vectors of a large matrix arises in many applications. This paper describes restarted block Lanczos bidiagonalization methods based on augmentation of Ritz vectors or harmonic Ritz vectors
The Generalized Schur Algorithm for the Superfast Solution of Toeplitz Systems
 in Rational Approximation and its Applications in Mathematics and Physics
, 1987
"... We review the connections between fast, O(n ), Toeplitz solvers and the classical theory of Szego polynomials and Schur's algorithm. ..."
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Cited by 23 (5 self)
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We review the connections between fast, O(n ), Toeplitz solvers and the classical theory of Szego polynomials and Schur's algorithm.
The Quadratic Eigenvalue Problem
, 2001
"... . We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skewHermitian) and t ..."
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Cited by 262 (21 self)
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. We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skewHermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software. Key words. quadratic eigenvalue problem, eigenvalue, eigenvector, matrix, matrix polynomial, secondorder differential equation, vibration, Millennium footbridge, overdamped system, gyroscopic system, linearization, backward error, pseudospectrum, condition number, Krylov methods, Arnoldi method, Lanczos method, JacobiDavidson method AMS subject classifications. 65F30 Contents 1 Introduction 2 2 Applications of QEPs 4 2.1 Secondorder differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Vibration analysis of structural systems ...
Results 1  10
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