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QR
Decomposition
Title: |
QR Decomposition |
Authors:
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Jose Divasón and
Jesús Aransay
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Submission date: |
2015-02-12 |
Abstract: |
QR decomposition is an algorithm to decompose a real matrix A into the product of two other matrices Q and R, where Q is orthogonal and R is invertible and upper triangular. The algorithm is useful for the least squares problem; i.e., the computation of the best approximation of an unsolvable system of linear equations. As a side-product, the Gram-Schmidt process has also been formalized. A refinement using immutable arrays is presented as well. The development relies, among others, on the AFP entry "Implementing field extensions of the form Q[sqrt(b)]" by René Thiemann, which allows execution of the algorithm using symbolic computations. Verified code can be generated and executed using floats as well. |
Change history: |
[2015-06-18]: The second part of the Fundamental Theorem of Linear Algebra has been generalized to more general inner product spaces. |
BibTeX: |
@article{QR_Decomposition-AFP,
author = {Jose Divasón and Jesús Aransay},
title = {QR Decomposition},
journal = {Archive of Formal Proofs},
month = feb,
year = 2015,
note = {\url{http://isa-afp.org/entries/QR_Decomposition.html},
Formal proof development},
ISSN = {2150-914x},
}
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License: |
BSD License |
Depends on: |
Gauss_Jordan, Rank_Nullity_Theorem, Real_Impl, Sqrt_Babylonian |
Status: [ok] |
This is a development version of this entry. It might change over time
and is not stable. Please refer to release versions for citations.
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