For pt.I, see Kibernetika, vol.13, no.6, p.28 (1977). Considerable effort was devoted in the surveyed period to automatic decomposition of sequential algorithms, or rather of procedures or subprograms written in the algorithmic languages ALGOL or FORTRAN. The authors do not consider this body of research, they only note that, on the one hand, the available linear algebra subprograms included in Eispack provide convenient objects for testing various approaches to automatic construction of parallel programs and, on the other, an important state in this activity is the development of methods for fast and efficient solution of linear recurrences, which reduce to solving systems of linear equations with band-triangular matrix (in particular, of sufficiently small width). This article reflects the penetration of the parallelism ideas into the computational methods of linear algebra in recent years. 74 references.

Parallel computations in linear algebra. II

Very large scale integration (VLSI) has evolved at an enormous rate, progressing from hundreds of components on an integrated circuit (IC) in the 1960's to a million components on a chip in the foreseeable future. This paper reviews some of the computer-aided design (CAD) tools that are essential for VLSI technology development and circuit design and that also require large amounts of computer resources. Specifically, we describe programs for process simulation, device simulation, and circuit simulation. This paper also reviews the impact of high-performance computing facilities on the development and use of these programs at AT & T Bell Laboratories.

The impact of supercomputers on IC technology development and design

Mathematical models for current vector processors are presented and the use of these models in performance evaluation discussed. Methods of defining vectors in the solution of sparse equations are summarized, and the vectorized solution of several classes of sparse problems are illustrated. Equation reordering based on symmetrical operations on a graph (folding, rotation) are shown to produce vectors in the solution. Finally, the use of a current vector processor, the CRAY-1, for the analysis of large integrated circuits is evaluated by examining the performance of kernels of a typical circuit analysis program.

Vector processors: Models and applications

References to Chapters 1 to 7

: This report describes a variety of assembly language codes developed for the CRAY-1 as part of general studies on implementation and use of linear algebra algorithms on vector machines. Included are descriptions of the performance and use of a vectorized general direct sparse equation solver, coding and performance of kernels arising from vector solution of subsystems of large sparse systems, and highly efficient 'gather' and 'scatter' codes useful in equation formulation. (Author)

D. A. Calahan

Papers

Sparse Matrix and Other High-Performance Algorithms for the CRAY-1.