Topics in Numerical Analysis
The nicer and practical parts of linear algebra, differential equations, and optimization.
Table of Contents
Numerical Linear Algebra
Numerical linear algebra is where rubber meets the road. This post collects some topics of interest to me. I aim to provide exposition better than standard textbooks whenever I can. Often times, ideas keep lying around deep inside 1000page bibles.
 Hutchinson Trace Estimator
 Cholesky decomposition
 Pivoted Cholesky decomposition
 Preconditioning
 Conjugate gradients
 Modified Batched Conjugate Gradient Descent
 Lanczos tridiagonalization
 Kroneckerfactored matrices
 Toeplitz matrices
 SzegÃ¶â€™s theorem
References
An uncategorized list of references of high pedagogic value.

An Introduction to the Conjugate Gradient Method Without the Agonizing Pain by Jonathan Richard Shewchuk (1994)

Toeplitz and Circulant Matrices: A Review by Robert M. Gray (2006)

Scalable Inference for Structured Gaussian Process Models, Chapter 5 ^{1} by Yunus SaatÃ§i (2011)

The Matrix Cookbook by Kaare Brandt Petersen, Michael Syskind Pedersen (2012)

Discovering Transforms: A Tutorial on Circulant Matrices, Circular Convolution, and the Discrete Fourier Transform by Bassam Bamieh (2018)
Lectures
 Scientific Computing for DPhil Students by Nick Trefethen (2016)
Textbooks

Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, III (1997)

Numerical Optimization by Jorge Nocedal, Stephen J. Wright (2006)
Footnotes

Includes description, properties and an application of Kroneckerfactored matrices. â†©