Let A/sub m/ be an m/spl times/m principal submatrix of an infinite-dimensional matrix A. We give a simple formula which expresses A/sub m+1//sup /spl minus/1/ in terms of A/sub m//sup /spl minus/1/, and based on this formula, an algorithm which computes the inverses of A/sub m/ for m=1, 2, 3, ..., n using only 2n/sup 3//spl minus/2n/sup 2/+n arithmetic operations. This is an improvement over the naive method of computing the inverses separately which would require /spl Sigma//sub m=1//sup n/ m/sup 3/=O(n/sup 4/) arithmetic operations.<>


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Inversion of all principal submatrices of a matrix


    Contributors:
    Koc, C.K. (author) / Chen, G. (author)


    Publication date :

    1994-01-01


    Size :

    266147 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Inversion of all Principal Submatrices of a Matrix

    Koç, Ç K. | Online Contents | 1994





    Efficiency of Generalized Matrix Inversion Methods

    F. C. Delaney / G. G. Gaffney / F. M. Speed | NTIS | 1966