Cholesky factorization and matrix inversion

Schmid, Erwin

i

Cholesky factorization and matrix inversion

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Personal Author:

Schmid, Erwin
Corporate Authors:

National Ocean Survey
NOAA Program & Office:

NOS (National Ocean Service)
Description:

The Cholesky square root algorithm used in the solution of linear equations with a positive definite matrix of coefficients is developed by elementary matrix algebra, independent of the Gaussian elimination from which it was originally derived. The Cholesky factorization leads to a simple inversion procedure for the given matrix. A simple transformation makes the inversion applicable to nonsymmetric matrices. The least squares hypothesis is shown to be the simplest and most general unique solution of a system of linear equations with a nonsquare matrix of coefficients. The method of proof is extended to develop the Gaussian elimination algorithm in a readily comprehensible procedure.
Keywords:

Mathematical Models Photogrammetry Satellite Triangulation Mathematical Models Satellite Triangulation
Series:

NOAA technical report NOS 56
Document Type:

Technical Report
Rights Information:

Public domain
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Library
Main Document Checksum:

urn:sha-512:452f66955dee35d8c68dfb04afee74bca48698c6a6d87806f05de35306781e6404aac636f3f82b6136a4efc9deee7743dddf983708d4f97612975f92008ec0a0
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https://repository.library.noaa.gov/view/noaa/30807/noaa_30807_DS1.pdf
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