Approximate Inversion Of Positive Definite Matrices, Specified On A Multiple Band

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Abstract
A fast algorithm is presented which can be used to compute an approximate inverse of a positive definite matrix if that matrix is specified only on a multiple band. The approximate inverse is the inverse of a matrix that closely matches the partially specified matrix. It has zeros in the positions that correspond to unspecified entries in the partially specified matrix. It is closely related to the so-called maximum-entropy extension of this matrix. The algorithm is very well suited for implementation on an array processor.
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