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# Accession Number:

## AD0672149

# Title:

## A DATA STRUCTURE CALCULUS FOR MATRICES,

# Descriptive Note:

# Corporate Author:

## BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH INFORMATION SCIENCES LAB

# Report Date:

## 1968-05-01

# Pagination or Media Count:

##
72.0

# Abstract:

## A matrix calculus is introduced with the intention to develop 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 avoiding superfluous operations. The power of the calculus is increased by introducing lists, lists of lists, etc. of matrices and by extending ordinary matrix operators to list operators and cumulative operators over lists. Effective algorithms are given which use symbolic manipulations of matrix and list 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. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#