TY - JOUR

T1 - Decell's finite algorithm for generalized inverses and tests to determine the rank of a matrix

AU - Kalaba, Robert

AU - Tishler, Asher

AU - Wang, Jia Song

PY - 1983

Y1 - 1983

N2 - This paper investigates the analytical and computational properties of Decell's[1] finite algorithm for determining the Moore-Penrose generalized inverse of a rectangular matrix. In Kalaba et al.[3] we show how Decell's algorithm, given by a finite sequence of matrices and scalars to be computed recursively, can be useful in the development of the algebraic properties of the Moore-Penrose generalized inverse. In this paper a complete characterization of the above sequence is given and proved. The analytical results are then used in developing three tests to determine the rank of a rectangular matrix. These tests (based on the computed matrices and scalars of the sequence) are empirically investigated and proved to be accurate.

AB - This paper investigates the analytical and computational properties of Decell's[1] finite algorithm for determining the Moore-Penrose generalized inverse of a rectangular matrix. In Kalaba et al.[3] we show how Decell's algorithm, given by a finite sequence of matrices and scalars to be computed recursively, can be useful in the development of the algebraic properties of the Moore-Penrose generalized inverse. In this paper a complete characterization of the above sequence is given and proved. The analytical results are then used in developing three tests to determine the rank of a rectangular matrix. These tests (based on the computed matrices and scalars of the sequence) are empirically investigated and proved to be accurate.

UR - http://www.scopus.com/inward/record.url?scp=0020951974&partnerID=8YFLogxK

U2 - 10.1016/0898-1221(83)90125-6

DO - 10.1016/0898-1221(83)90125-6

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AN - SCOPUS:0020951974

SN - 0898-1221

VL - 9

SP - 679

EP - 686

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 5

ER -