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Compression policy for Newton-like iteration of structured matrices

Ai-Long Zheng
Gianni Codevico
Victor Y. Pan
Marc Van Barel
Xinmao Wanga

2004 International Mathematica Symposium
Conference location

Banff, Canada

We review different adaptations of Newton’s iteration for computing the inverse or the Moore–Penrose generalized inverse of a matrix. Then we specialize this approach to the case of structured (and particularly Toeplitz or Toeplitz-like) matrices where all input,output and intermediate auxiliary matrices are represented in a compressed form,via their short displacement generators. We briefly recall the well known policies of compression via the truncation of the smallest singular values of the displacement and via substitution and elaborate upon the more recent policy of the least-squares compression.

*Mathematics > Algebra > Linear Algebra

compression policy, structured matrices, Moore-Penrose generalized inverse, Toeplitz, truncation
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