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.