Computational Improvements to Matrix Operations

Details Computational Improvements to Matrix Operations Computational Improvements to Matrix Operations

2006-01-18

arxiv.org/abs/physics/0601134v1

Physics

General Physics

6 pages, LaTeX

Scientific paper

An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a vector in ${\cal O}(N)$. This is in contrast to the usual ${\cal O}(N^3)$ and ${\cal O}(N^2)$. A finite size bit register can lead to speeds up of an order of magnitude in large matrices such as $500\times 500$. The FFT can be improved from ${\cal O}(N\ln N)$ to ${\cal O}(N)$ steps, or even fewer steps in a modified butterfly configuration.

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