On derivative estimation and the solution of least squares problems

Nonparametric Least Squares Estimation in Derivative Families

Cost function estimation often involves data on a function and a family of its derivatives. It is known that by using such data the convergence rates of nonparametric estimators can be substantially improved. In this paper we propose series-type estimators which incorporate various derivative data into a single, weighted, nonparametric, least-squares procedure. Convergence rates are obtained, w...

On the Least Squares Solution of Inverse Eigenvalue Problems

An inverse eigenvalue problem where a matrix is to be constructed from some or all of its eigenvalues may not have a real valued solution at all An approximate solution in the sense of least squares is sometimes desirable Two types of least squares problems are formulated and explored in this paper In spite of their di erent appearance the two problems are shown to be equivalent Thus one new nu...

Solution of Nonlinear Least Squares Problems on a Multiprocessor

In this paper we describe algorithms for solving nonlinear least squares problems on a message-passing multiprocessor. We demonstrate new parallel algorithms, including an efficient parallel algorithm for determining the Levenberg-Marquardt parameter and a new row-oriented QR factorization algorithm. Experimental results obtained on an Intel iPSC h ~ r c u b e are presented and compared with se...

Solving Derivative-Free Nonlinear Least Squares Problems with POUNDERS

Least squares collocation solution of elliptic problems in general regions

7 We consider the solution of elliptic problems in general regions by embedding and least squares approximation of overdetermined 8 collocated tensor product of basis functions. The resulting least squares problem will generally be ill-conditioned or even singular, 9 and thus, regularization techniques are required. Large scale problems are solved by either conjugate gradient type methods or by...