Software for Roundoff Analysis of Matrix Algorithms

Computer Science and Applied Mathematics: A Series of Monographs and Textbooks: Software for Roundoff Analysis of Matrix Algorithms focuses on the presentation of techniques and software tools for analyzing the propagation of rounding error in matrix algorithms. The publication looks into some elements of error analysis, concepts from linear algebra and analysis, and directed graphs. Discussions focus on arithmetic graphs, sums of path products, linear transformations, Minkowski sums and Cartesian products, and elementary concepts from analysis. The text then examines software for roundoff analysis, including rounding and perturbations of the computational problem, comparing rounding errors with problem sensitivity, reverse condition numbers, and comparing two algorithms. The book ponders on case studies, as well as Gaussian elimination with iterative improvement, Cholesky factorization, Gauss-Jordan elimination, variants of the Gram-Schmidt method, and Cholesky factors after rank-one modifications. The text is a valuable reference for researchers interested in the techniques and software tools involved in the analysis of the propagation of rounding error in matrix algorithms.