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

作者：Abderraman Marrero J; Tomeo V^*

来源：Journal of Computational and Applied Mathematics, 2017, 318: 211-219.

DOI：10.1016/j.cam.2016.10.004

• Accuracy
• Bordered k-tridiagonal matrix
• Givens rotation
• Matrix linear equation

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 = B. The (n x n) matrix coefficient A is a nonsingular bordered k-tridiagonal matrix. The particular structure of A is exploited through an incomplete or full Givens reduction, depending on the singularity of its associated k-tridiagonal matrix. Then adapted back substitution and Sherman Morrison's formula can be applied. Specially the inverse of the matrix A is computed. Moreover for a wide range of matrices A, the solution of the vector linear equation Ax = b can be computed in 0(n) time. Numerical comparisons illustrate the results.

• 出版日期2017-7