Numerical Linear Algebra Algorithms Research Articles

The weak and strong stability of algorithms in numerical linear algebra

The stability of algorithms in numerical linear algebra is discussed. The concept of stability is extended to notions of weak stability and strong stability. Justifications are given for these extensions, and the implications of error analyses in terms of these definitions are discussed. The concept of weak stability helps to clarify some of the controversy which has arisen concerning the stability of algorithms for Toeplitz systems.

Effectivity and optimizing of algorithms and programs on the host-computer/array-processor system

This paper examines the performance and implementation of algorithms on host-computer/attached array-processor systems. A performance analysis method for such systems is reviewed with the application to the host-computer EC 1045/array-processor EC 2345 system produced in the USSR. The relative performance comparison of different algorithms on the EC 1045-EC 2345 system is presented and the effectiveness of algorithms and optimal evaluation of programs is discussed. The results are demonstrated on several numerical linear algebra algorithms. Theoretical results are compared with numerical experiments.

A Survey of Parallel Algorithms in Numerical Linear Algebra

The existence of parallel and pipeline computers has inspired a new approach to algorithmic analysis. Classical numerical methods are generally unable to exploit multiple processors and powerful vector-oriented hardware. Efficient parallel algorithms can be created by reformulating familiar algorithms or by discovering new ones, and the results are often surprising. A comprehensive survey of parallel techniques for problems in linear algebra is given. Specific topics include: relevant computer models and their consequences for programs, evaluation of arithmetic expressions, solution of general and special linear systems of equations, and computation of eigenvalues.