The purpose of this paper is to develop and analyze a least-squares approximation to a first order system. The first order system represents a reformulation of a second order elliptic boundary value problem which may be indefinite and/or nonsymmetric. The approach taken here is novel in that the least-squares functional employed involves a discrete inner product which is related to the inner pr...

This article presents how to use the least-squares (LS) regression method to price the American options on basis of the algorithm in a paper by Clement, Lamberton & Protter[1]. The key to LS is the approximation of the conditional expectation functions which determine the optimal exercise strategy. In this paper, through the detailed description of the algorithm and presentation of convergence,...

In previous work we introduced a construction to produce biorthogonal multiresolutions from given subdivisions. The approach involved estimating the solution to a least squares problem by means of a number of smaller least squares approximations on local portions of the data. In this work we use a result by Dahlquist, et. al. on the method of averages to make observational comparisons between t...

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance measure between the approximate minimizer and the true minimizer (solution approx...

In this paper a new least-squares (LS) approach is used to model the discrete-time fractional differintegrator. This approach is based on a mismatch error between the required response and the one obtained by the difference equation defining the auto-regressive, moving-average (ARMA) model. In minimizing the error power we obtain a set of suitable normal equations that allow us to obtain the AR...

The reduced basis method is a projection technique for approximating the solution curve of a finite system of nonlinear algebraic equations by the solution curve of a related system that is typically of much lower dimension. In this paper, the reduced basis error is shown to be dominated by an approximation error. This, in turn, leads to error estimates for projection onto specific subspaces: f...

Approximation of the solution of an ill-posed spherical pseudo-differential equation at a given point Abstract This paper presents a method for approximating the solution of an ill-posed spherical pseudo-differential equation at a given point. The approximation is based on the regularized least-squares method of An et. al., We discuss an a posteriori parameter choice rule and illustrate our the...

We present a method for computing partial spectra of Hermitian matrices, based on a combination of subspace iteration with rational filtering. In contrast with classical rational filters derived from Cauchy integrals or from uniform approximations to a step function, we adopt a least-squares (LS) viewpoint for designing filters. One of the goals of the proposed approach is to build a filter tha...