Abstract
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×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 O(n) time. Numerical comparisons illustrate the results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.