ON THE TEXTURED ITERATIVE ALGORITHMS FOR A CLASS OF TRIDIAGONAL LINEAR-EQUATIONS

The textured, iterative approximation algorithms are a class fast line ar equation solvers [1], [2] and differ from the classical iterative a lgorithms fundamentally in their approximations of system matrices. Th e textured approach uses different approximations of a system matrix i n a round-robin fashion while the classical approaches use a single fi xed approximation. It therefore has a better approximation of system m atrix and a potentially faster speed. In this note we prove that the c onvergent speed of the textured iterative algorithms for linear equati ons with a class of tridiagonal system matrices is strictly faster tha n the corresponding classical iterative algorithms. We also give the s pectral radii of the textured iterative and classical algorithms for t his class of linear equations. These results provide some insights and theoretical supports for the textured iterative algorithms.