Bennani M. and Braconnier T., (1994a), Comparative behaviour of eigensolvers on highly nonnormal matrices, Tech. Rep. TR/PA/94/23, CERFACS. Home/Search Document Details and Download
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Arnoldi versus Nonsymmetric Lanczos Algorithms for Solving.. - Cullum (1996) (6 citations) (Correct)
....symmetric Lanczos recursion, We would like to be able to answer the question: What spectral properties of A control the convergence of each of these methods We have not answered this question but describe several results which might be useful in such studies. See for example, the related work [2, 3, 4, 5, 6, 7, 8, 27, 28, 29]. In section 2 we outline briefly the Arnoldi and the nonsymmetric Lanczos eigenvalue procedures we are considering. In section 3 we exhibit a certain relationship between these two methods. We prove that given any matrix A and any application of a nonsymmetric Lanczos procedure to A, there exists ....
M. Bennani and T. Braconnier, Comparative behaviour of eigensolvers on highly nonnormal matrices. CERFACS Technical Report TR-PA-94-23 (1994). CERFACS, Toulouse, France.
Parallel Computation of Spectral Portraits on the Meiko CS2 - Frayssé, Giraud, Toumazou (1996) (Correct)
.... that N = fz 2 l C ; k(A Gamma zI) Gamma1 k 2 kAk 2 Gamma1 g [12] The level curve fz 2 l C ; k(A Gamma zI) Gamma1 k 2 kAk 2 = Gamma1 g is the border of the pseudospectrum of A and corresponds to the set of eigenvalues corresponding to a backward error equal to (see [1]) So N is the set of all approximate eigenvalues of A associated with a backward error less than or equal to . The spectral portrait, introduced by Godunov [9] consists in the representation of z Gamma spp(z) log 10 k(A Gamma zI) Gamma1 k 2 kAk 2 in the complex plane. Its ....
M. Bennani and T. Braconnier. Comparative behaviour of eigensolvers on highly nonnormal matrices. Tech. Rep. TR/PA/94/23, CERFACS, 1994.
Influence of Orthogonality on the Backward Error and the.. - Braconnier (1995) (1 citation) Self-citation (Braconnier) (Correct)
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M. Bennani and T. Braconnier, (1994a), Comparative behaviour of eigensolvers on highly nonnormal matrices, Tech. Rep. TR/PA/94/23, CERFACS.
Is Nonnormality a Serious Computational Difficulty in Practice? - Chaitin-Chatelin (Correct)
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Bennani M. and Braconnier T., (1994a), Comparative behaviour of eigensolvers on highly nonnormal matrices, Tech. Rep. TR/PA/94/23, CERFACS.
Is Nonnormality a Serious Difficulty? - Chaitin-Chatelin (Correct)
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M. Bennani and T. Braconnier, (1993a), Comparative behaviour of eigensolvers on highly nonnormal matrices. Submitted to IMA J. Numer. Anal.
Spectral Portait Computation by a Lanczos Method (Augmented.. - MARQUES, TOUMAZOU (Correct)
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M. Bennani and T. Braconnier, (1993a), Comparative behaviour of eigensolvers on highly nonnormal matrices. Submitted to Jour. Num. Lin. Alg. Appl.
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