An iterative method for solving nonlinear least squares problems with nondifferentiable operator

Preconditioned Iterative Methods for Solving Linear Least Squares Problems

New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...

Solving Derivative-Free Nonlinear Least Squares Problems with POUNDERS

On Iterative Krylov-Dogleg Trust-Region Steps for Solving Neural Networks Nonlinear Least Squares Problems

This paper describes a method of dogleg trust-region steps, or restricted Levenberg-Marquardt steps, based on a projection process onto the Krylov subspaces for neural networks nonlinear least squares problems. In particular, the linear conjugate gradient (CG) method works as the inner iterative algorithm for solving the linearized Gauss-Newton normal equation, whereas the outer nonlinear algor...

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...

Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm i...