Adaptive filter theory
Hyperbolic householder transforms
SIAM Journal on Matrix Analysis and Applications
Robust regression computation computation using iteratively reweighted least squares
SIAM Journal on Matrix Analysis and Applications
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Displacement structure: theory and applications
SIAM Review
Stabilizing the Generalized Schur Algorithm
SIAM Journal on Matrix Analysis and Applications
Stability Issues in the Factorization of Structured Matrices
SIAM Journal on Matrix Analysis and Applications
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A System of Subroutines for Iteratively Reweighted Least Squares Computations
ACM Transactions on Mathematical Software (TOMS)
Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem
SIAM Journal on Matrix Analysis and Applications
Blind Deconvolution Using a Regularized Structured Total Least Norm Algorithm
SIAM Journal on Matrix Analysis and Applications
On the Stability of the Generalized Schur Algorithm
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems
SIAM Journal on Matrix Analysis and Applications
Benchmark testing of algorithms for very robust regression: FS, LMS and LTS
Computational Statistics & Data Analysis
Hi-index | 0.03 |
The problem of computing an approximate solution of an overdetermined system of linear equations is considered. The usual approach to the problem is least squares, in which the 2-norm of the residual is minimized. This produces the minimum variance unbiased estimator of the solution when the errors in the observations are independent and normally distributed with mean 0 and constant variance. It is well known, however, that the least squares solution is not robust if outliers occur, i.e., if some of the observations are contaminated by large error. In this case, alternate approaches have been proposed which judge the size of the residual in a way that is less sensitive to these components. These include the Huber M-function, the Talwar function, the logistic function, the Fair function, and the @?"1 norm. New algorithms are proposed to compute the solution to these problems efficiently, in particular, when the matrix A has small displacement rank. Matrices with small displacement rank include matrices that are Toeplitz, block-Toeplitz, block-Toeplitz with Toeplitz blocks, Toeplitz plus Hankel, and a variety of other forms. For exposition, only Toeplitz matrices are considered, but the ideas apply to all matrices with small displacement rank. Algorithms are also presented to compute the solution efficiently when a regularization term is included to handle the case when the matrix of the coefficients is ill-conditioned or rank-deficient. The techniques are illustrated on a problem of FIR system identification.