Numerical solutions of symmetric saddle point problem by direct methods

• Autorzy: Smoktunowicz A. , Okulicka-Dłużewska F.
• Języki publikacji: EN

Abstrakty

EN

Numerical stability of two main direct methods for solving the symmetric saddle point problem are analyzed. The first one is a generalization of Golub’s method for the augmented system formulation (ASF) and uses the Householder QR decomposition. The second method is supported by the singular value decomposition (SVD). Numerical comparison of some direct methods are given.

Słowa kluczowe

EN

saddle point problem; Householder transformation; QR decomposition; singular values; backward error; condition number

PL

punkt siodłowy; przekształcenie Householdera; rozkład QR; wartość liczby pojedynczej

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 3
• Strony: 437--451
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Smoktunowicz A.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, Warsaw, 00-662, Poland

autor

Okulicka-Dłużewska F.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, Warsaw, 00-662, Poland

Bibliografia

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• [3] Å. Björck, C. C. Paige, Solution of augmented linear systems using orthogonal factorizations, BIT 34 (1994), 1–24.
• [4] Å. Björck, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA, USA, 1996.
• [5] B. N. Datta, Numerical Linear Algebra and Applications, SIAM, Philadelphia, PA, USA, 2010.
• [6] J. W. Demmel, Applied Numerical Linear Algebra, SIAM, Philadelphia, PA, USA, 1997.
• [7] N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, PA, USA, 1996.
• [8] G. H. Golub, Ch. F. Van Loan, Matrix Computations, Third Edition, The Johns Hopkins University Press, Baltimore and London, 1996.
• [9] A. M. Ostrowski, On some metrical properties of operator matrices and matrices partitioned into blocks, J. Math. Anal. Appl. 2 (1961), 161–209.
• [10] A. Smoktunowicz, Blockwise analysis for solving linear systems of equations, J. KSIAM 3(1) (1999), 31–41.
• [11] A. Smoktunowicz, Block matrices and symmetric perturbations, Linear Algebra Appl. 429 (2008), 2628–2635.
• [12] M. Szularz, A. Smoktunowicz, E. Pawelec, An inverse structured perturbation problem for the linear system AT Ax=b, Demonstratio Math. 43(4) (2010), 755–763.