Block Computations and Verified Numerical Computations for Linear Systems

摘要

This talk is concerned with verified numerical computations for linear systems. It is known that if block computations are applied for L U decomposition and triangular systems, then upper bounds of residuals of them are reduced. We present block implementation for these problems with arbitrary block size and apply them to the verification of the numerical solutions of the linear systems. As a result, the treatable range for our method is wider than that for an original method.