Real time system parameter estimation from the set of input-output data is usually solved by the quadratic norm minimization of system equations errors known as least squares (LS). But measurement errors are also in the data matrix and so it is necessary to use a modification known as total least squares (TLS) or mixed LS and TLS. Instead of quadratic norm minimization other p-norms are used, f...

Support vector machines (SVMs), have proven to be effective for solving learning problems, and have been successfully applied to a large number of tasks. Lately a new technique, the Least Squares SVM (LS-SVM) has been introduced. This least squares version simplifies the required computation, but sparseness –a really attractive feature of the standard SVM– is lost. To reach a sparse model, furt...

Least squares support vector machines (LS-SVM) is an SVM version which involves equality instead of inequality constraints and works with a least squares cost function. In this way, the solution follows from a linear Karush–Kuhn–Tucker system instead of a quadratic programming problem. However, sparseness is lost in the LS-SVM case and the estimation of the support values is only optimal in the...

Introduction and Summary The use of regression analysis relies on the choice of a criterion in order to estimate the coefficients of the explanatory variables. Traditionally, the least squares (LS) criterion has been the method of choice. However, the least absolute value (LAV) criterion provides an alternative. LAV regression coefficients are chosen to minimize the sum of the absolute values o...

Diffuse optical tomography (DOT) involves estimation of tissue optical properties using noninvasive boundary measurements. The image reconstruction procedure is a nonlinear, ill-posed, and ill-determined problem, so overcoming these difficulties requires regularization of the solution. While the methods developed for solving the DOT image reconstruction procedure have a long history, there is l...

Minimum residual norm iterative methods for solving linear systems Ax = b can be viewed as, and are often implemented as, sequences of least squares problems involving Krylov subspaces of increasing dimensions. The minimum residual method (MINRES) [C. Paige and M. Saunders, SIAM J. Numer. Anal., 12 (1975), pp. 617–629] and generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIA...