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

Qun Lin & Wujian Peng

DOI: 10.4208/aamm.10-m1162

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 = {Lin , Qun and Peng , Wujian}, 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} }
TY - JOUR T1 - An Acceleration Method for Stationary Iterative Solution to Linear System of Equations AU - Lin , Qun AU - Peng , Wujian JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 473 EP - 482 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m1162 UR - https://global-sci.org/intro/article_detail/aamm/131.html KW - Iterative method, error analysis, recurrence. AB -

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.

Lin , Qun and Peng , Wujian. (2012). An Acceleration Method for Stationary Iterative Solution to Linear System of Equations. Advances in Applied Mathematics and Mechanics. 4 (4). 473-482. doi:10.4208/aamm.10-m1162
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