Numerical methods for finding stationary gravitational solutions

Numerical Methods in Gravitational Lensing

Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or distortion; (2) propagating light rays through large cosmological simulations; and (3) reconstructing mass distributions from their tidal field. This lecture descr...

Numerical Methods for Evolution and Stationary (Integro-)Differential Equations

This study-research project is about numerical methods of differential equations (ordinary differential equations (ODE), partial differential equation (PDE), and integro-differential equations (IDE).) Required courses for this project are Math 212/213 (Multivariable Calculus), Math 302 (Differential Equations); and additional training in Math 345 (Introduction in Mathematical Biology), Math 413...

Some Notes with Numerical Methods for Stationary Pdes

Componentwise Error Estimates for Solutions Obtained by Stationary Iterative Methods

In stationary iterative methods for solving linear systems Ax = b, the iteration x = Hx + c, where H and c are the iteration matrix derived from A and the vector derived from A and b, respectively, is executed for an initial vector x. We present a theorem which yields componentwise error estimates for x, and clarify the relation between our result and a previous result.

Lagrangian-based methods for finding MAP solutions for MRF models

Finding maximum a posteriori (MAP) solutions from noisy images based on a prior Markov random field (MRF) model is a huge computational task. In this paper, we transform the computational problem into an integer linear programming (ILP) problem. We explore the use of Lagrange relaxation (LR) methods for solving the MAP problem. In particular, three different algorithms based on LR are presented...