Updating the inverse of a matrix
Updating the inverse of a matrix - compare online religious dating services
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Four different approaches are developed, implemented, and tested on a number of numerical experiments. The S-M formula is important in many different fields of numerical computation; see for example [2–7].On the other hand, Toeplitz matrices arise in a number of various theoretical investigations and applications.A number of iterative processes for finding generalized inverses of an arbitrary Toeplitz matrix by modifying Newton’s method have been developed so far. Adaptations of the iterative processes to the Toeplitz structure are based on the usage of the displacement operator as well as the concept of displacement representation and -displacement rank of matrices.The fastest is an inverse matrix update where only one element of the source matrix is changed. The inverse matrix update by row or column is only 2 times slower (thus, if three or more elements of one row or column were modified, it would better to use this algorithm than the previous one). The inverse matrix update with arbitrary vectors u and v is three times slower than the simple update. At least, one step is stable enough if A and B are well-conditioned. The Sherman--Morrison--Woodbury formulas relate the inverse of a matrix after a small-rank perturbation to the inverse of the original matrix.