An Error Model for Swarztrauber’s Parallel Tridiagonal Equation Solver
Nai–Kuan Tsao · SIAM Journal on Matrix Analysis and Applications · 1994
Error models for two algorithms based on Cramer’s rule are given for tridiagonal systems. The results show that if the exact $x_i $ of the solution vector x is expressed as $\det p/\det q$ where p and q are matrices formed from the original coefficient matrix and the right-hand side vector, then the computed $x_i $ can be expressed as $\det \hat p/\det \hat q$, where $\det \hat p$ and $\det \hat q$ are perturbed $\det p$ and $\det q$, respectively, using either the parallel or the sequential algorithm. The relative error of each product in the determinantal expansion of $\det \hat p$ and $\det \hat q$ can also be bounded easily.