A \(Krylov\) subspace generalization of the improved 详细信息    查看全文

• 作者：Majid Adib
• 关键词：Linear system ; Iterative method ; Ill ; conditioned problems ; \(Wilkinson\) ; ’s method ; \(Krylov\) ; subspace method
• 刊名：Calcolo
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：53
• 期：1
• 页码：51-58
• 全文大小：376 KB
• 参考文献：1.Dongarra, J., Sullivan, F.: Guest editors introduction to the top 10 algorithms. Comput. Sci. Eng. 2(1), 22–23 (2000)CrossRef
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  3.Glub, G.H., Van Loan, C.F.: Matrix Computation, 3rd edn. John Hopkins University Prees, Baltimore (1996)
  4.Martin, R.S., Peters, G., Wilkinson, J.H.: Iterative refinement of the solution of a positive definite system of equations. In: Baner, F.L. (ed.) Handbook for Automatic Computation, Linear Algebra, vol. II. Springer, Berlin (1971)
  5.Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis, p. 207. Springer, New York (1980)CrossRef
  6.Wilkinson, J.H.: Rounding Errors in Algebraic Processes. Prentice-Hall, Engle-Wood cliffs (1963)MATH
  7.Wu, X., Shao, R., Xue, G.: Iterative refinement of solution with biparameter for solving ill-condition systems of linear algebraic equations. Appl. Math. Comput. 131, 235–244 (2002)CrossRef MathSciNet MATH
  8.Zhang, F.: Matrix Theory: Basic Results and Techniques, Secound edn. Linear Park, Davie (2011)CrossRef
  
• 作者单位：Majid Adib (1)
  
  1. Department of Mathematics, Faculty of Sciences, University of Zanjan, 45195-313, Zanjan, Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Theory of Computation
  
• 出版者：Springer Milan
• ISSN：1126-5434

文摘

An extension of improved \({ Wilkinson}\)’s algorithm for solving ill-conditioned linear system is proposed. We show that our algorithm belongs to the preconditioned \(Krylov\) subspace class. Then, we offer some useful preconditioners to reduce the condition number of the coefficient matrix of linear equations and increase the rate of convergence of algorithm. Finally, we present some numerical experiments to show the efficiency and accuracy of our algorithm on ill-conditioned problems.