Solving Least Squares Problems
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 problems of their own discipline. This well-organized presentation of the basic material needed for the solution of least squares problems can unify this divergence of methods. Mathematicians, practising engineers, and scientists will welcome its return to print. The material covered includes Householder and Givens orthogonal transformations, the QR and SVD decompositions, equality constraints, solutions in nonnegative variables, banded problems, and updating methods for sequential estimation. Both the theory and practical algorithms are included. The easily understood explanations and the appendix providing a review of basic linear algebra make the book accessible for the non-specialist.
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Algorithm HFTI Anal Appendix application arithmetic array named augmented matrix BNDACC bounds candidate solution Chapter Cholesky column vectors components condition number constraints covariance matrix defined denote diagonal elements diagonal matrix eigenvalues equations error euclidean example execute Algorithm Fortran go to Step Golub Hansen Householder transformation inequality integers least squares problem least squares solution Lemma Linear Algebra linear least squares m x n matrix m-vector Math mathematical matrix Q method minimal minimum length solution n x n NETLIB Nonlinear nonsingular nonzero obtained orthogonal matrix output perturbation problem Ax Problem LS Problem LSE pseudoinverse pseudorank QR algorithm QR decomposition quantities rank Rank(A residual norm residual vector rows satisfy Section sequential SIAM singular value analysis singular value decomposition solution vector solving storage array submatrix subroutine subspace symmetric matrix Theorem tion unique variables Wilkinson zero