Continuous Dependence of Least Squares Solutions of Linear Boundary Value Problems

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

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 ...

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

Wavelet Least Squares Methods for Boundary Value Problems

Solving Continuous Linear Least-Squares Problems by Iterated Projection

I present a new divide-and-conquer algorithm for solving continuous linear least-squares problems. The method is applicable when the column space of the linear system relating data to model parameters is “translation invariant”. The central operation is a matrixvector product, which makes the method very easy to implement. Secondly, the structure of the computation suggests a straightforward pa...