An extension of the domain of the APL domino function to rank deficient linear least squares systems

Authors:
Augustin A. Dubrulle
Affiliations:
-
Venue:
APL '75 Proceedings of seventh international conference on APL
Year:
1975

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Abstract

This paper presents an extension of the domain of the APL Domino function to systems of linear equations the matrix of which contains linearly dependent columns. This extension is based on the concepts of minimum and basic least squares solutions, and pseudo-inverses [1,2], which have found many applications in various areas such as statistics [3] and mathematical programming [4]. In the following, basic definitions and properties of least squares solutions and pseudo-inverses are summarized, and a formal description of the proposed algorithms is illustrated with APL formulations and results of test runs. The necessary mathematical background and the details of the methods briefly described here are contained in the References.