# 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.

The history of these formulas is presented and various applications to statistics, networks, structural analysis, asymptotic analysis, optimization, and partial differential equations are discussed.Below are the most common reasons: This site uses cookies to improve performance by remembering that you are logged in when you go from page to page.To provide access without cookies would require the site to create a new session for every page you visit, which slows the system down to an unacceptable level.This problem is also known as inpainting in the context of image processing and for this purpose we suggest an iterative sparse recovery algorithm based on constrained l1-norm minimization with a new fidelity metric.The incorporated metric called Convex SIMilarity (CSIM) index is a simplified version of the Structural SIMilarity (SSIM) index which is convex and error-sensitive.The optimization problem incorporating this criterion is then solved via Alternating Direction Method of Multipliers (ADMM).