Approximate Inversion of Partially Specified Positive Definite Matrices

A fast algorithm is presented that can be used to compute an approximate inverse of a positive definite matrix that 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 inverse of the so-called maximum-entropy extension of the partially specified matrix. The algorithm is very well suited for implementation on an array processor.