Multiplicative Error Analysis of Matrix Transformation Algorithms

The author's recently introduced relative error measure forvectors is applied to the error analysis of algorithms whichproceed by successive transformation of a matrix. Instead ofmodelling the roundoff errors at each stage by A: = T(A)+E onemodels them by A: =e^E T(A) where E is a small linear transformation.This can simplify analyses considerably. Applications to theparallel Jacobi method for eigenvalues, and to Gaussian elimination,are given.