A fast and reliable numerical solver for general bordered -tridiagonal matrix linear equations

详细信息    查看全文

• 作者：J. Abderramá ; n Marrerop>ap>p> ; p>p>jc.abderraman@upm.esp> ; V. Tomeop>bp>p> ; p>p>tomeo@ucm.esp>
• 关键词：15A06 ; 15A23 ; 15B99 ; 65F99
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：211-219
• 全文大小：503 K
• 卷排序：318

文摘

To improve on the shortcomings observed in symbolic algorithms introduced recently for related matrices, a reliable numerical solver is proposed for computing the solution of the matrix linear equation AX=BAX=B. The (n×n)(n×n) matrix coefficient AA is a nonsingular bordered kk-tridiagonal matrix. The particular structure of AA is exploited through an incomplete or full Givens reduction, depending on the singularity of its associated kk-tridiagonal matrix. Then adapted back substitution and Sherman–Morrison’s formula can be applied. Specially the inverse of the matrix AA is computed. Moreover for a wide range of matrices AA, the solution of the vector linear equation Ax=bAx=b can be computed in O(n)O(n) time. Numerical comparisons illustrate the results.