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Numerical methods for least square problems
Preface 1. Mathematical and statistical properties of least squares solutions 2. Basic numerical methods 3. Modified least squares problems . Expand
Solving linear least squares problems by Gram-Schmidt orthogonalization
AbstractA general analysis of the condition of the linear least squares problem is given. The influence of rounding errors is studied in detail for a modified version of the Gram-SchmidtExpand
Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations
Iterative methods are developed for computing the Moore-Penrose pseudoinverse solution of a linear systemAx=b, whereA is anm ×n sparse matrix. The methods do not require the explicit formation ofATAExpand
Loss and Recapture of Orthogonality in the Modified Gram-Schmidt Algorithm
This paper arose from a fascinating observation, apparently by Charles Sheffield, and relayed to us by Gene Golub, that the QR factorization of an $m \times n$ matrix A via the modified Gram-Schmidt algorithm (MGS) is numerically equivalent to that arising from Householder transformations applied to the matrix A augmented by an n by n zero matrix. Expand
Numerical Methods in Matrix Computations
Direct Methods for Linear Systems.- Linear Least Squares Problems.- Matrix Eigenvalue Problems.- Iterative Methods.
Solution of Vandermonde Systems of Equations
We obtain in this paper a considerable improvement over a method developed earlier by Ballester and Pereyra for the solution of systems of linear equations with Vandermonde matrices of coefficients.Expand
Numerical methods in scientific computing
List of figures List of tables List of conventions Preface 1. Expand
A Schur method for the square root of a matrix
Abstract A fast and stable method for computing the square root X of a given matrix A ( X 2 = A ) is developed. The method is based on the Schur factorization A = QSQ H and uses a fast recursion toExpand