Abstract
We recall Newton’s iteration for computing the inverse or Moore–Penrose generalized inverse of a matrix. Then we specialize this approach to the case of structured matrices where all input, output and intermediate auxiliary matrices are represented in a compressed form, via their short displacement generators. We design a new Newton-like iteration based on a cubic polynomial and show its effectiveness by some numerical experiments for matrices from the Toeplitz-like class and the Cauchy-like class.
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Codevico, G., Pan, V.Y. & Van Barel, M. Newton-Like Iteration Based on a Cubic Polynomial for Structured Matrices. Numer Algor 36, 365–380 (2004). https://doi.org/10.1007/s11075-004-3996-z
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DOI: https://doi.org/10.1007/s11075-004-3996-z