Numerical Methods for Least Squares Problems by Ake Bjõrck

By Ake Bjõrck

The strategy of least squares used to be chanced on by way of Gauss in 1795. It has when you consider that develop into the vital instrument for decreasing the impression of mistakes while becoming versions to given observations. this present day, purposes of least squares come up in loads of clinical components, equivalent to facts, geodetics, sign processing, and keep an eye on.

In the final twenty years there was an excellent raise within the ability for computerized facts shooting and computing. Least squares difficulties of huge measurement are actually sometimes solved. super development has been made in numerical equipment for least squares difficulties, particularly for generalized and converted least squares difficulties and direct and iterative equipment for sparse difficulties. previously there has no longer been a monograph that covers the complete spectrum of correct difficulties and strategies in least squares.

This quantity provides an in-depth therapy of issues comparable to equipment for sparse least squares difficulties, iterative tools, transformed least squares, weighted difficulties, and limited and regularized difficulties. The greater than 800 references offer a entire survey of the on hand literature at the topic.

Show description

Read or Download Numerical Methods for Least Squares Problems PDF

Best elementary books

Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion

This is an outline of recent computational stabilization equipment for linear inversion, with purposes to a number of difficulties in audio processing, scientific imaging, seismology, astronomy, and different components. Rank-deficient difficulties contain matrices which are precisely or approximately rank poor. Such difficulties usually come up in reference to noise suppression and different difficulties the place the target is to suppress undesirable disturbances of given measurements.

Calculus: An Applied Approach

Designed particularly for enterprise, economics, or life/social sciences majors, Calculus: An utilized technique, 8/e, motivates scholars whereas fostering figuring out and mastery. The ebook emphasizes built-in and interesting functions that express scholars the real-world relevance of subject matters and ideas.

Algebra, Logic and Combinatorics

This publication leads readers from a easy origin to a sophisticated point figuring out of algebra, good judgment and combinatorics. ideal for graduate or PhD mathematical-science scholars searching for assist in figuring out the basics of the subject, it additionally explores extra particular components comparable to invariant concept of finite teams, version idea, and enumerative combinatorics.

Additional resources for Numerical Methods for Least Squares Problems

Sample text

CHOLESKY FACTORIZATION (ROW-WISE VERSION). , they will compute the same factor R, even taking rounding errors into account. We remark that from it follows that the elements in R are bounded in terms of the diagonal elements in C. This is essential for the numerical stability of the Cholesky factorization. 1.

A relationship between the Cholesky factorization of ATA and the QR decomposition of A is given next. 20 CHAPTER 1. 2. Let A e R mxn have rank n. Then if the R-factor in the QR decomposition of A has positive diagonal elements it equals the Cholesky factor ofATA. 4 the Cholesky factor of ATA is unique. 2) it follows that which concludes the proof. 4) Hence we can express Q\ uniquely in terms of A and R. However the matrix Q<2 will not, in general, be uniquely determined. 5) which shows that the columns of Q\ and $2 form orthonormal bases for Tl(A) and its complement.

17) is as useful as the SVD. 5. 7. 24 CHAPTER 1. 4. Sensitivity of Least Squares Solutions In this section we give results on the sensitivity of pseudoinverses and least squares solutions to perturbations in A and b. Many of the results below were first given by Wedin [824, 1973]. Stewart in [731, 1977] gives a unified treatment with interesting historical comments on the perturbation theory for pseudoinverses and least squares solutions. A more recent and excellent source of information is Stewart and Sun [754, 1990, Chap.

Download PDF sample

Rated 4.17 of 5 – based on 3 votes