Volume 4, Issue 4
An Acceleration Method for Stationary Iterative Solution to Linear System of Equations

Qun Lin & Wujian Peng

Adv. Appl. Math. Mech., 4 (2012), pp. 473-482.

Published online: 2012-04

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  • Abstract

An acceleration scheme based on stationary iterative methods is presented for solving linear system of equations. Unlike Chebyshev semi-iterative method which requires accurate estimation of the bounds for iterative matrix eigenvalues, we use a wide range of Chebyshev-like polynomials for the accelerating process without estimating the bounds of the iterative matrix. A detailed error analysis is presented and convergence rates are obtained. Numerical experiments are carried out and comparisons with classical Jacobi and Chebyshev semi-iterative methods are provided.

  • Keywords

Iterative method error analysis recurrence

  • AMS Subject Headings

65F10 15A06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-473, author = {Qun Lin and Wujian Peng}, title = {An Acceleration Method for Stationary Iterative Solution to Linear System of Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {4}, pages = {473--482}, abstract = {

An acceleration scheme based on stationary iterative methods is presented for solving linear system of equations. Unlike Chebyshev semi-iterative method which requires accurate estimation of the bounds for iterative matrix eigenvalues, we use a wide range of Chebyshev-like polynomials for the accelerating process without estimating the bounds of the iterative matrix. A detailed error analysis is presented and convergence rates are obtained. Numerical experiments are carried out and comparisons with classical Jacobi and Chebyshev semi-iterative methods are provided.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1162}, url = {http://global-sci.org/intro/article_detail/aamm/131.html} }
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