Least squares, singular values and matrix approximations

Singular Values and Least Squares Matching

In this paper we investigate least squares matching problems, extending the methods of our earlier paper 1] in such a way as to make them applicable to problems involving the sets of points that are so complex that approximate answers are of interest. These problems are formulated in terms of continuous descent equations, and lower bounds on the quality of the best match are obtained in terms o...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Least squares approximations of power series

The classical least squares solutions in C[−1,1] in terms of linear combinations of ul-traspherical polynomials are extended in order to estimate power series on (−1,1). Approximate rates of uniform and pointwise convergence are obtained, which correspond to recent results of U. Luther and G. Mastroianni on Fourier projections with respect to Jacobi polynomials.

Regularization of singular least squares problems

In this note we analyze the in uence of the regularization procedure applied to singular LS square problems It appears that due to nite numerical accuracy within the computer calculations the regularization parameter has to belong to a particular range of values in order to have the regularized solution close to that associated to the singular LS problem Surprisingly enough this range essential...

Least-Squares Covariance Matrix Adjustment

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...