Multiplicative Error Analysis of Matrix Transformation Algorithms
John D. Pryce · IMA Journal of Numerical Analysis · 1985
The author's recently introduced relative error measure for vectors is applied to the error analysis of algorithms which proceed by successive transformation of a matrix. Instead of modelling the roundoff errors at each stage by A: = T(A)+E one models them by A: =eE T(A) where E is a small linear transformation. This can simplify analyses considerably. Applications to the parallel Jacobi method for eigenvalues, and to Gaussian elimination, are given.