A Variable Projection Method for Solving Separable Nonlinear Least Squares Problems

Variable projection for nonlinear least squares problems

The variable projection algorithm of Golub and Pereyra (1973) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a better likelihood of finding a global minimizer rather than a local one. The purpose of our work is to provide a more robust implementat...

Separable Nonlinear Least Squares: the Variable Projection Method and its Applications

Randomized Block Kaczmarz Method with Projection for Solving Least Squares

The Kaczmarz method is an iterative method for solving overcomplete linear systems of equations Ax = b. The randomized version of the Kaczmarz method put forth by Strohmer and Vershynin iteratively projects onto a randomly chosen solution space given by a single row of the matrix A and converges exponentially in expectation to the solution of a consistent system. In this paper we analyze two bl...

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...

Randomized Algorithms for Solving Large Scale Nonlinear Least Squares Problems

This thesis presents key contributions towards devising highly efficient stochastic reconstruction algorithms for solving large scale inverse problems, where a large data set is available and the underlying physical systems is complex, e.g., modeled by partial differential equations (PDEs). We begin by developing stochastic and deterministic dimensionality reduction methods to transform the ori...