On the solution of rank deficient least squares problems

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Title: On the solution of rank deficient least squares problems
Author: Lira, Mark J.
Abstract: In this thesis , we introduce a new method for solving minimum norm least squares problems . This method involves a QR decomposition followed by a Cholesky decomposition (QC ) . The existing methods in the literature are the Complete Orthogonal Factorization which involves two QR decompositions , and the SVD method . We compare the computational requirements of our method to the Complete Orthogonal Factorization method and show that QC requires fewer ops as long as the matrix is rank deficient . We also compare the sensitivity of the solution obtained by our method and the Complete Orthogonal Factorization method to parameter perturbations for generic matrices . A Kolmogorov -Smirnov test was run on the results of numerical experiments using normally distributed parameter perturbations . The results showed that the Null Hypothesis that the solutions by both algorithms have the same continuous underlying distribution cannot be rejected to a significance level of 0 .05 . The same numerical experiments showed that for the full rank case , the normal equation method using a Cholesky decomposition is significantly computationally faster than the QR method .
URI: http : / /hdl .handle .net /2346 /ETD -TTU -2011 -08 -1885
Date: 2011-08

Citation

On the solution of rank deficient least squares problems. Master's thesis, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /ETD -TTU -2011 -08 -1885 .

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