A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation | Zendy

Junxia Hou | Zendy; LV Quan-yi | Zendy; Manyu Xiao | Zendy

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A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation

Author(s) -

Junxia Hou,

LV Quan-yi,

Manyu Xiao

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/598716

Subject(s) - conjugate gradient method , algorithm , computer science , matrix (chemical analysis) , mathematics , chemistry , chromatography

Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modified form of conjugate gradient (MCG) method. Furthermore, Schur’s inequality and modified conjugate gradient method are employed to overcome the involved difficulties such as determination of parameter and calculation of inverse matrix. Several numerical results finally show that high performance of proposed parallel algorithm is obtained both in convergent rate and in parallel efficiency

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