Cholesky decomposition

In place matrix factorization

This is an implementation of Cholesky decomposition based on [1]. The algorithm exploits matrix multiplication and is consequently faster than the canonical implementations of Cholesky decomposition via Cholesky-Banachiewicz/Cholesky-Crout decompositions, which use only matrix-vector multiplication (and not matrix-matrix multiplication). Interestingly enough, the algorithm can be seen as a hybrid between Cholesky-Banachiewicz and Cholesky-Crout algorithms. The algorithm takes a parameter, which says how large should be the matrix for matrix multiplication. If no parameter is passed, an optimal size for matrix multiplication is estimated.

The package contains following algorithms:
1) Cholesky-Banachiewicz
2) Cholesky-Crout
3) Hybrid

A practical note: Neither of the implementations is faster than the build in 'chol' function. The provided methods are merely for educative purposes.

[1] Simple, Fast and Practicable Algorithms for Cholesky, LU and QR Decomposition Using Fast Rectangular Matrix Multiplication by Cristóbal Camarero