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Solving Least Squares Problems (Prentice-Hall Series in Automatic Computation)

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Charles L. Lawson

Solving Least Squares Problems (Prentice-Hall Series in Automatic Computation) First Edition

  • ISBN-10 0138225850
  • ISBN-13 978-0138225858
  • Edition First Edition
  • Publisher Prentice Hall
  • Publication date January 1, 1974
  • Language English
  • Print length 340 pages
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  • Publisher ‏ : ‎ Prentice Hall; First Edition (January 1, 1974)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 340 pages
  • ISBN-10 ‏ : ‎ 0138225850
  • ISBN-13 ‏ : ‎ 978-0138225858
  • Item Weight ‏ : ‎ 1.39 pounds
  • #9,390 in Mathematics (Books)
  • #136,233 in Unknown

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solving least squares problems lawson

Charles L. Lawson

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Richard J. Hanson

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solving least squares problems lawson

Solving least squares problems

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Solving least squares problems

40,785  citations

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Cites methods from "Solving least squares problems"

... They solve the subproblems in CP-ALS and Tucker-ALS with a specially adapted version of the NNLS method of Lawson and Hanson [150]. ...

7,828  citations

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... In particular, Forward Stagewise ideas are used in “boosting,” an important class of fitting methods for data mining introduced by Freund and Schapire (1997) . ...

... all positive. If not, one or more variables are dropped [using the inner loop of the NNLS algorithm described in Lawson and Hanson (1974) ], again requiring downdating of Rk. With many correlated variables, the stagewise version can take many more steps than LARS because of frequent dropping and adding of variables, increasing the computations by a factor up to 5 or more in extreme cases. ...

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Solving least squares problems (classics in applied mathematics, series number 15) - softcover, lawson, charles l. ; hanson, richard j..

9780898713565: Solving Least Squares Problems (Classics in Applied Mathematics, Series Number 15)

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  • Publisher Society for Industrial and Applied Mathematics
  • Publication date 1987
  • ISBN 10  0898713560
  • ISBN 13  9780898713565
  • Binding Paperback
  • Number of pages 350
  • Rating 4.67 avg rating • ( 3 ratings by Goodreads )

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lawson , a FORTRAN77 code which solves least squares problems, by Charles Lawson, Richard Hanson,

The most common least squares problems considers an overdetermined M by N linear system A*X=B. A least squares solution X is sought which has the property that, although it generally is not a solution of the system, it is the best approximation to a solution, in the sense that it minimizes the L2 norm of the residual R=A*X-B.

In some cases, a unique solution to the system A*X=B will exist, and in that case the least squares solution will coincide with what is ordinarily meant by a solution.

In underdetermined cases, where multiple solutions exist, the least squares solution is usually taken to be that solution X which has minimum L2 norm, that is, which minimizes ||X||.

The original FORTRAN77 source code is available through NETLIB at https://www.netlib.org/lawson-hanson/index.html .

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

lawson is available in a FORTRAN77 version and a FORTRAN90 version .

Related Data and Programs:

lawson_test

brent , a FORTRAN77 library which contains Richard Brent's routines for finding the zero, local minimizer, or global minimizer of a scalar function of a scalar argument, without the use of derivative information.

BVLS , a FORTRAN90 library which applies least squares methods to solve a linear system for which lower and upper constraints may have been placed on every variable.

DQED , a FORTRAN77 library which solves constrained least squares problems.

NL2SOL , a FORTRAN77 library which implements an adaptive nonlinear least-squares algorithm.

PRAXIS , a FORTRAN77 library which minimizes a scalar function of several variables.

QR_SOLVE , a FORTRAN77 library which computes the least squares solution of a linear system A*x=b.

TEST_LS , a FORTRAN77 library which implements linear least squares test problems of the form A*x=b.

TOMS581 , a FORTRAN77 library which implements an improved algorithm for computing the singular value decomposition (SVD) of a rectangular matrix; this is ACM TOMS algorithm 571, by Tony Chan.

TOMS611 , a FORTRAN77 library which seeks the minimizer of a scalar functional of multiple variables.

  • Gene Golub, Christian Reinsch, Singular Value Decomposition and Least Squares Solutions, Numerische Mathematik, Volume 14, Number 5, April 1970, pages 403-420.
  • Charles Lawson, Richard Hanson, Solving Least Squares Problems, Revised edition, SIAM, 1995, ISBN: 0898713560, LC: QA275.L38.

LAWSON Least Squares Routines

LAWSON is a FORTRAN77 library which can solve least squares problems.

The most common least squares problems considers an overdetermined M by N linear system A*X=B. A least squares solution X is sought which has the property that, although it generally is not a solution of the system, it is the best approximation to a solution, in the sense that it minimizes the L2 norm of the residual R=A*X-B.

In some cases, a unique solution to the system A*X=B will exist, and in that case the least squares solution will coincide with what is ordinarily meant by a solution.

In underdetermined cases, where multiple solutions exist, the least squares solution is usually taken to be that solution X which has minimum L2 norm, that is, which minimizes ||X||.

The original FORTRAN77 source code is available through NETLIB at http://www.netlib.org/lawson-hanson/index.html .

LAWSON is available in a FORTRAN77 version and a FORTRAN90 version .

Related Data and Programs:

BRENT , a FORTRAN77 library which contains Richard Brent's routines for finding the zero, local minimizer, or global minimizer of a scalar function of a scalar argument, without the use of derivative information.

BVLS , a FORTRAN90 library which applies least squares methods to solve a linear system for which lower and upper constraints may have been placed on every variable.

DQED , a FORTRAN77 library which solves constrained least squares problems.

NL2SOL , a FORTRAN77 library which implements an adaptive nonlinear least-squares algorithm.

PRAXIS , a FORTRAN77 library which minimizes a scalar function of several variables.

QR_SOLVE , a FORTRAN77 library which computes the least squares solution of a linear system A*x=b.

TEST_LS , a FORTRAN77 library which implements linear least squares test problems of the form A*x=b.

TOMS581 , a FORTRAN77 library which implements an improved algorithm for computing the singular value decomposition (SVD) of a rectangular matrix; this is ACM TOMS algorithm 571, by Tony Chan.

TOMS611 , a FORTRAN77 library which seeks the minimizer of a scalar functional of multiple variables.

  • Gene Golub, Christian Reinsch, Singular Value Decomposition and Least Squares Solutions, Numerische Mathematik, Volume 14, Number 5, April 1970, pages 403-420.
  • Charles Lawson, Richard Hanson, Solving Least Squares Problems, Revised edition, SIAM, 1995, ISBN: 0898713560, LC: QA275.L38.

Source Code:

  • lawson.f , the source code.
  • lawson.sh , commands to compile the source code.

Examples and Tests:

  • lawson_prb1.f , a sample problem.
  • lawson_prb1.sh , commands to compile, link and run the sample problem.
  • lawson_prb1_output.txt , the output file.
  • lawson_prb2.f , a sample problem.
  • lawson_prb2.sh , commands to compile, link and run the sample problem.
  • lawson_prb2_output.txt , the output file.
  • lawson_prb3.f , a sample problem.
  • lawson_prb3.sh , commands to compile, link and run the sample problem.
  • lawson_prb3_output.txt , the output file.
  • lawson_prb4.f , a sample problem.
  • lawson_prb4.sh , commands to compile, link and run the sample problem.
  • lawson_prb4_input.txt , the input file.
  • lawson_prb4_output.txt , the output file.
  • lawson_prb5.f , a sample problem.
  • lawson_prb5.sh , commands to compile, link and run the sample problem.
  • lawson_prb5_output.txt , the output file.
  • lawson_prb6.f , a sample problem.
  • lawson_prb6.sh , commands to compile, link and run the sample problem.
  • lawson_prb6_output.txt , the output file.

List of Routines:

  • BNDACC accumulates information for a banded least squares problem.
  • BNDSOL solves a banded least squares problem accumulated by BNDACC.
  • DIFF is used in tests that depend on machine precision.
  • G1 computes an orthogonal rotation matrix.
  • G2 applies a rotation matrix to a vector (X,Y).
  • GEN generates numbers for construction of test cases.
  • H12 constructs or applies a Householder transformation.
  • HFTI Householder forward triangulation with column interchanges.
  • LDP implements least distance programming
  • MFEOUT labeled matrix output for use with singular value analysis.
  • NNLS implements the nonnegative least squares algorithm.
  • QRBD uses the QR algorithm for the singular values of a bidiagonal matrix.
  • SVA carries out a singular value analysis.
  • SVDRS singular value decomposition also treating right side vector.

You can go up one level to the FORTRAN77 source codes .

IMAGES

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  3. Solving Least Squares Problems (Charles L. Lawson and Richard J. Hanson)

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  4. (PDF) TNT-NN: A Fast Active Set Method for Solving Large Non-Negative Least Squares Problems

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COMMENTS

  1. Solving Least Squares Problems

    Description An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. This book has served this purpose well.

  2. Solving least squares problems : Lawson, Charles L : Free Download

    Solving least squares problems by Lawson, Charles L. Publication date 1974 Topics Least squares -- Data processing Publisher Englewood Cliffs, N.J., Prentice-Hall Collection inlibrary; printdisabled; internetarchivebooks Contributor Internet Archive Language English. xii, 340 p. 24 cm Bibliography: p. 312-326

  3. [PDF] Solving least squares problems

    C. Lawson, R. Hanson Published in Classics in applied… 1 July 1976 Mathematics Since the lm function provides a lot of features it is rather complicated. So we are going to instead use the function lsfit as a model. It computes only the coefficient estimates and the residuals.… Expand View via Publisher stats.ox.ac.uk Save to Library Create Alert

  4. Solving Least Squares Problems

    Solving Least Squares Problems Charles L. Lawson, Richard J. Hanson Prentice-Hall, 1974 - Mathematics - 340 pages Analysis of the least squares problem. Orthogonal decomposition by...

  5. Solving Least Squares Problems

    Charles L. Lawson, Richard J. Hanson SIAM, Dec 1, 1995 - Mathematics - 349 pages An accessible text for the study of numerical methods for solving least squares problems remains an essential...

  6. Solving Least Squares Problems

    01 06 Keywords 511'.42—dc20 Keywords QA275.L38 1995Least squares—Data processing Affiliations Charles L. Lawson

  7. Solving Least Squares Problems

    Solving Least Squares Problems Charles L. Lawson, Richard J. Hanson Society for Industrial and Applied Mathematics, 1995 - Mathematics - 337 pages An accessible text for the study of numerical...

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    Solving Least Squares Problems - Ebook written by Charles L. Lawson, Richard J. Hanson. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline...

  9. Solving Least Squares Problems (Prentice-Hall Series in Automatic

    Solving Least Squares Problems (Prentice-Hall Series in Automatic Computation) First Edition by Charles L. Lawson (Author) 3.9 3.9 out of 5 stars 10 ratings

  10. PDF Least Squares Problems

    A good reference on this topic can be found in the book, Solving Least Squares Problems, by Lawson and Hanson. 4.1 Linear Least Square Problems. Example. (Polynomial Fitting) Let (zi, yi), i = 1, . . . , m be the observed quantities. Suppose the function f in (4.1) is an (n 1)-th degree polynomial. −.

  11. PDF least squares problems

    BJORCK Wepresent some generalized QRfactorizations which can be used to different generalized least squares problems. Many applications lead to L8 problems where the solution isubject to constraints. This includes linear equality and inequality constraints. Quadratic constraints are used to regu larize solutions o discrete ill-posed problems.

  12. Solving Least Squares Problems by Charles L. Lawson

    Charles L. Lawson, Richard J. Hanson. An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. This book has served this purpose well. Numerical analysts, statisticians, and engineers have developed techniques and nomenclature for the least squares ...

  13. Solving least squares problems by Charles L. Lawson

    November 17, 2022. Edited by ImportBot. import existing book. April 1, 2008. Created by an anonymous user. Imported from Scriblio MARC record . Solving least squares problems by Charles L. Lawson, 1974, Prentice-Hall edition, in English.

  14. Solving Least Squares Problems (Prentice-Hall Series in Automatic

    An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. This book has served this purpose well. ... Texas. Charles Lawson retired from the Jet Propulsion Propulsion Laboratory of the California Institute of Technology (Caltech) in October, 1996. He ...

  15. Solving Least Squares Problems

    Solving Least Squares Problems. Charles L. Lawson, Richard J. Hanson. SIAM, Dec 1, 1995 - Mathematics - 349 pages . ... Solving Least Squares Problems Charles L. Lawson, Richard J. Hanson Limited preview - 1995. Solving Least Squares Problems Charles L. Lawson, Richard J. Hanson Snippet view - 1974.

  16. Solving least squares problems

    Solving least squares problems Charles L. Lawson, Richard J. Hanson 31 May 1974 - TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals. View 20 related papers

  17. LAWSON

    LAWSON is a FORTRAN90 library which solves least squares problems.. The most common least squares problems considers an overdetermined M by N linear system A*X=B. A least squares solution X is sought which has the property that, although it generally is not a solution of the system, it is the best approximation to a solution, in the sense that it minimizes the L2 norm of the residual R=A*X-B.

  18. Solving Least Squares Problems (Charles L. Lawson and Richard J. Hanson

    Get full access to this article. View all available purchase options and get full access to this article.

  19. Solving Least Squares Problems (Classics in Applied ...

    Featured Edition ISBN 10: ISBN 13: 9780138225858 Publisher: Prentice Hall, 1974 Hardcover Search for all books with this author and title Top Search Results from the AbeBooks Marketplace Solving Least Squares Problems (Classics in Applied Mathematics, Series Number 15) Lawson, Charles L.

  20. lawson

    lawson, a FORTRAN77 code which solves least squares problems, by Charles Lawson, Richard Hanson, . The most common least squares problems considers an overdetermined M by N linear system A*X=B. A least squares solution X is sought which has the property that, although it generally is not a solution of the system, it is the best approximation to a solution, in the sense that it minimizes the L2 ...

  21. Solving Least Squares Problems

    Charles L. Lawson, Richard J. Hanson Prentice-Hall, 1974 - Electronic data processing - 340 pages 0 Reviews Reviews aren't verified, but Google checks for and removes fake content when it's...

  22. LAWSON

    LAWSON is a FORTRAN77 library which can solve least squares problems.. The most common least squares problems considers an overdetermined M by N linear system A*X=B. A least squares solution X is sought which has the property that, although it generally is not a solution of the system, it is the best approximation to a solution, in the sense that it minimizes the L2 norm of the residual R=A*X-B.

  23. TNT-NN: A Fast Active Set Method for Solving Large Non-Negative Least

    In 1974 Lawson and Hanson produced a seminal active set strategy to solve least-squares problems with non-negativity constraints that remains popular today. ... Solving least squares problems. 2nd edition, 1995. [15] E.A. Lima, B.P. Weiss, L. Baratchart, D.P. Hardin, and E.B. Saff. Fast inversion of magnetic field maps of unidirectional planar ...