Matrix black box algorithms - a survey

The implementations of matrix multiplication on contemporary, vector-oriented, and multicore-oriented computer hardware are very carefully designed and optimized with respect to their efficiency, due to the essential significance of that operation in other science and engineering domains. Consequent...

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Published inBulletin of the Polish Academy of Sciences. Technical sciences Vol. 70; no. 2
Main Author Jerzy Respondek
Format Journal Article
LanguageEnglish
Published Polish Academy of Sciences 01.04.2022
Subjects
matrix algebra
matrix multiplication algorithm
numerical recipes
recursion
Online AccessGet full text
ISSN2300-1917
0239-7528
2300-1917
DOI10.24425/bpasts.2022.140535

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Abstract The implementations of matrix multiplication on contemporary, vector-oriented, and multicore-oriented computer hardware are very carefully designed and optimized with respect to their efficiency, due to the essential significance of that operation in other science and engineering domains. Consequently, the available implementations are very fast and it is a natural desire to take advantage of the efficiency of those implementations in other problems, both matrix and nonmatrix. Such an approach is often called a black box matrix computation paradigm in the literature on the subject. In this article, we gathered a broad series of algorithms taking advantage of the efficiency of fast matrix multiplication algorithms in other mathematical and computer science operations.
AbstractList The implementations of matrix multiplication on contemporary, vector-oriented, and multicore-oriented computer hardware are very carefully designed and optimized with respect to their efficiency, due to the essential significance of that operation in other science and engineering domains. Consequently, the available implementations are very fast and it is a natural desire to take advantage of the efficiency of those implementations in other problems, both matrix and nonmatrix. Such an approach is often called a black box matrix computation paradigm in the literature on the subject. In this article, we gathered a broad series of algorithms taking advantage of the efficiency of fast matrix multiplication algorithms in other mathematical and computer science operations.
Author Jerzy Respondek
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recursion
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