Parallel Algorithms for Linear Models

Kontoghiorghes, Erricos John

doi:10.1007/978-1-4615-4571-2

Cited by 24 publications

(4 citation statements)

References 90 publications

(224 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerically, this is equivalent to downdating an orthogonal matrix decomposition after a column has been deleted (Golub and Van Loan 1996;Kontoghiorghes 2000;Smith and Bremner 1989). Givens rotations are employed to efficiently move from one node to another.…”

Section: Computational Strategiesmentioning

confidence: 99%

lmSubsets: Exact Variable-Subset Selection in Linear Regression for R

Hofmann¹,

Gatu²,

Kontoghiorghes³

et al. 2020

J. Stat. Soft.

View full text Add to dashboard Cite

An R package for computing the all-subsets regression problem is presented. The proposed algorithms are based on computational strategies recently developed. A novel algorithm for the best-subset regression problem selects subset models based on a predetermined criterion. The package user can choose from exact and from approximation algorithms. The core of the package is written in C++ and provides an efficient implementation of all the underlying numerical computations. A case study and benchmark results illustrate the usage and the computational efficiency of the package.

show abstract

Section: Computational Strategiesmentioning

confidence: 99%

lmSubsets: Exact Variable-Subset Selection in Linear Regression for R

Hofmann¹,

Gatu²,

Kontoghiorghes³

et al. 2020

J. Stat. Soft.

View full text Add to dashboard Cite

show abstract

“…One of them uses QR decomposition of the matrix M [19], [20], [21], [22]. The QR decomposition method has the advantage of stability with regard to propagating data errors [19], [20], [21].…”

Section: Least-squares Solutionmentioning

confidence: 99%

“…(3.22) we use a QR decomposition of matrix H. This factorization expresses the matrix H eis the product of em orthogonzil matrix and an upper-triangular matrix [31]. The QR decomposition is computed using the Householder transformation method [22], [23], [31]. The QR decomposition allows us to trajisform the problem into an upper-triangular system of equations which is solved by backsubstitution.…”

Section: Least-squares Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Regularization of the image division approach to blind deconvolution

Barraza-Felix

Frieden

1999

Appl. Opt.

View full text Add to dashboard Cite

In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicrte the deletion. COMMITTEE ON OPTICAL SCIENCES (GRADUATE)In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHYIn the Graduate College THE UNIVERSITY OF ARIZONA STATEMENT BY AUTHORThis dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona £md is deposited in the University Library to be made available to borrowers under rules of the Library.Brief quotations from this dissertation are allowable without special jjermission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholeirship. In all other instances, however, permission must be obtained from the author. SIGNED: ACKNOWLEDGMENTSFirst I have to thank my family for giving me the necessary strength to complete this rough journey.I owe a great debt to my advisor Dr. B. Roy Rrieden. Thanks to his guidance and patience I could finish this work.I especially must thank Dr. Shoemacker and the OSC staff, in particular Didi Lawson, who always help me without hesitation.I also want to thank Candido Pinto. He was the one who helped me to overcome most of the computer related problems that I confronted during this work.This research would not have been possible without the support of CONACYT (Mexico), and the University of Sonora (Mexico). DEDICATIONTo the memory of my mother.To my father. for 14 pixels support, (c) for 12 pixels supp., (d) for 10 pixels supp., (e) for 8 pixels supp., (f) for 6 pixels supp., (g) for 4 pixels supp., (h) for 2 pixels supp 45 FIGURE 3.5. Flow chart for the image division program 48 It is found that the system of linear equations, resulting from the implementation of the image division method, has a multiplicity of solutions. Moreover such sj'stem of equations is poorly conditioned. This brings the necessity of a regularization approach.This dissertation describes the development and implementation of a regulariza tion algorithm for the image division method. Using this regularization algorithm the blind deconvolution problem is posed eis a constrained lezist-squares problem. A least-squares solution is fovmd by computing a QR factorization of the system matrix.The Householder transformation method is used to find this factorization. The QR decomposition transforms the problem into an upper-triangular system of equations which is solved by bcicksubstitution. Prior pzirtial knowledge about the point-spread fimctions and the object (such as finite support and positivity) is used to impose constrziins on the solution, solving the multiplicity-solutions problem. 15The...

show abstract

Computationally E.cient Methods for Solving SURE Models

Kontoghiorghes

Foschi

2001

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Parallel Algorithms for Linear Models

Cited by 24 publications

References 90 publications

lmSubsets: Exact Variable-Subset Selection in Linear Regression for R

lmSubsets: Exact Variable-Subset Selection in Linear Regression for R

Regularization of the image division approach to blind deconvolution

Computationally E.cient Methods for Solving SURE Models

Contact Info

Product

Resources

About