TY - JOUR

T1 - On Recursive Calculation of the Generalized Inverse of a Matrix

AU - Mohideen, Saleem

AU - Cherkassky, Vladimir

PY - 1991/1/3

Y1 - 1991/1/3

N2 - The generalized inverse of a matrix is an extension of the ordinary square matrix inverse which applies to any matrix 1991. The generalized inverse has numerous important applications such as regression analysis, filtering, optimization and, more recently, linear associative memories. In this latter application known as Distributed Associative Memory, stimulus vectors are associated with response vectors and the result of many associations is spread over the entire memory matrix, which is calculated as the generalized inverse. Addition/deletion of new associations requires recalculation of the generalized inverse, which becomes computationally costly for large systems. A better solution is to calculate the generalized inverse recursively. The proposed algorithm is a modification of the well known algorithm due to Rust et al. [2], originally introduced for nonrecursive computation. We compare our algorithm with Greville's recursive algorithm and conclude that our algorithm provides better numerical stability at the expense of little extra computation time and additional storage.

AB - The generalized inverse of a matrix is an extension of the ordinary square matrix inverse which applies to any matrix 1991. The generalized inverse has numerous important applications such as regression analysis, filtering, optimization and, more recently, linear associative memories. In this latter application known as Distributed Associative Memory, stimulus vectors are associated with response vectors and the result of many associations is spread over the entire memory matrix, which is calculated as the generalized inverse. Addition/deletion of new associations requires recalculation of the generalized inverse, which becomes computationally costly for large systems. A better solution is to calculate the generalized inverse recursively. The proposed algorithm is a modification of the well known algorithm due to Rust et al. [2], originally introduced for nonrecursive computation. We compare our algorithm with Greville's recursive algorithm and conclude that our algorithm provides better numerical stability at the expense of little extra computation time and additional storage.

KW - associative data retrieval

KW - associative memory

KW - recursive algorithm

UR - http://www.scopus.com/inward/record.url?scp=0026115395&partnerID=8YFLogxK

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U2 - 10.1145/103147.103160

DO - 10.1145/103147.103160

M3 - Article

AN - SCOPUS:0026115395

SN - 0098-3500

VL - 17

SP - 130

EP - 147

JO - ACM Transactions on Mathematical Software (TOMS)

JF - ACM Transactions on Mathematical Software (TOMS)

IS - 1

ER -