dorsal/arxiv
View SchemaComputational Improvements to Matrix Operations
| Authors | Gordon Chalmers |
|---|---|
| Categories | |
| ArXiv ID | physics/0601134 |
| URL | https://arxiv.org/abs/physics/0601134 |
Abstract
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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"abstract": "An alternative to the matrix inverse procedure is presented. Given a bit\nregister which is arbitrarily large, the matrix inverse to an arbitrarily large\nmatrix can be peformed in ${\\cal O}(N^2)$ operations, and to matrix\nmultiplication on a vector in ${\\cal O}(N)$. This is in contrast to the usual\n${\\cal O}(N^3)$ and ${\\cal O}(N^2)$. A finite size bit register can lead to\nspeeds up of an order of magnitude in large matrices such as $500\\times 500$.\nThe FFT can be improved from ${\\cal O}(N\\ln N)$ to ${\\cal O}(N)$ steps, or even\nfewer steps in a modified butterfly configuration.",
"arxiv_id": "physics/0601134",
"authors": [
"Gordon Chalmers"
],
"categories": [
"physics.gen-ph"
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"title": "Computational Improvements to Matrix Operations",
"url": "https://arxiv.org/abs/physics/0601134"
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