THE BLOCK LSMR ALGORITHM FOR SOLVINGLINEAR SYSTEMS WITH MULTIPLERIGHT-HAND SIDES

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TOUTOUNIAN F.; MOJARRAB M.

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Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2015 | Volume:5 | Issue:2 Page(s): 11-28

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Information Journal Paper

Title

THE BLOCK LSMR ALGORITHM FOR SOLVINGLINEAR SYSTEMS WITH MULTIPLERIGHT-HAND SIDES

Author(s)

TOUTOUNIAN F. | MOJARRAB M. | Issue Writer Certificate

Keywords

LSMR METHODQ2

BIDIAGONALIZATIONQ2

BLOCK METHODSQ2

ITERATIVEMETHODSQ3

MULTIPLE RIGHT-HAND SIDESQ2

Abstract

LSMR (Least Squares Minimal Residual) is an iterative method for thesolution of the linear system of equations and least-squares problems. Thispaper presents a block version of the LSMR algorithm for solving linear sys-tems with MULTIPLE RIGHT-HAND SIDES. The new algorithm is based on the blockBIDIAGONALIZATION and derived by minimizing the Frobenius norm of the resid-ual matrix of normal equations. In addition, the convergence of the proposedalgorithm is discussed. In practice, it is also observed that the Frobeniusnorm of the residual matrix decreases monotonically. Finally, numerical ex-periments from real applications are employed to verify the e ectiveness ofthe presented method.

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APA: Copy

TOUTOUNIAN, F., & MOJARRAB, M.. (2015). THE BLOCK LSMR ALGORITHM FOR SOLVINGLINEAR SYSTEMS WITH MULTIPLERIGHT-HAND SIDES. IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION, 5(2 ), 11-28. SID. https://sid.ir/paper/260837/en

Vancouver: Copy

TOUTOUNIAN F., MOJARRAB M.. THE BLOCK LSMR ALGORITHM FOR SOLVINGLINEAR SYSTEMS WITH MULTIPLERIGHT-HAND SIDES. IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION[Internet]. 2015;5(2 ):11-28. Available from: https://sid.ir/paper/260837/en

IEEE: Copy

F. TOUTOUNIAN, and M. MOJARRAB, “THE BLOCK LSMR ALGORITHM FOR SOLVINGLINEAR SYSTEMS WITH MULTIPLERIGHT-HAND SIDES,” IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION, vol. 5, no. 2 , pp. 11–28, 2015, [Online]. Available: https://sid.ir/paper/260837/en

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