A least squares solution to linear boundary value problems with impulses

Fully Nonlinear Boundary Value Problems with Impulses

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth...

Linear Least Squares Problems

A fundamental task in scientific computing is to estimate parameters in a mathematical model from collected data which are subject to errors. The influence of the errors can be reduced by using a greater number of data than the number of unknowns. If the model is linear, the resulting problem is then to “solve” an in general inconsistent linear system Ax = b, where A ∈ Rm×n and m ≥ n. In other ...

A fast algorithm for linear least-squares smoothing and boundary value problems using number-theoretic transforms

A fast algorithm for linear least-squares smoothing and boundary value problems using number-theoretic transforms (NTT) is presented. The algorithm utilizes the fact that the fixed interval smoother can be imbedded in a boundary value problem, which can be reformulated as a problem of solving a perturbed-circulant system of equations. The new algorithm solves this perturbed-circulant system of ...

Wavelet Least Squares Methods for Boundary Value Problems

Computational Investigations of Least-Squares Type Methods for the Approximate Solution of Boundary Value Problems

Several Galerkin schemes for approximate solution of linear elliptic boundary value problems are studied for such computational aspects as obtainable accuracy, sensitivity to parameters and conditioning of linear systems. Methods studied involve computing subspaces (e.g., splines) whose elements need not satisfy boundary conditions. A Poisson problem study on the square produces computed error ...