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Author Witzgall, Christoph ♦ Bayer, Rudolf
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Matrix ♦ Symbol manipulation ♦ Complete calculus ♦ Matrix seqences ♦ Matrix concatenation ♦ Data structures ♦ Linear programming ♦ Sequence operations ♦ Programming languages
Abstract A matrix calculus is introduced with the intention of developing data structures suitable for a high level algorithmic language for mathematical programming. The paper investigates how the special structure of matrices can be described and utilized for efficient computing by saving memory space and superfluous operations.Sequences of matrices (and sequences of sequences of matrices) are considered, and matrix operators are extended to sequence operators and cumulative operators.Algorithms are given which use symbol manipulation of matrix expressions so as to find the forms best suited for computation. These forms are called normal forms. Several completeness results are obtained in the sense that for each expression an equivalent expression in normal form can be found within a specified calculus.
Description Affiliation: Boeing Scientific Research Lab, Seattle, WA (Bayer, Rudolf; Witzgall, Christoph)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 13
Issue Number 4
Page Count 15
Starting Page 223
Ending Page 237


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Source: ACM Digital Library