# Modified Recursive Cholesky (Rchol) Algorithm: An Explicit Estimation and Pseudo-inverse of Correlation Matrices

## TL;DR

This paper introduces a modified recursive Cholesky (RChol) algorithm for explicit estimation and pseudo-inversion of correlation matrices, offering a potentially faster and stable alternative to traditional methods like SVD and LU.

## Contribution

It presents a new recursive algorithm for Cholesky decomposition that improves estimation of correlation matrices compared to conventional methods.

## Key findings

- RChol algorithm provides accurate correlation matrix estimation.
- It demonstrates computational efficiency over traditional methods.
- The method enhances numerical stability in matrix inversion.

## Abstract

The Cholesky decomposition plays an important role in finding the inverse of the correlation matrices. As it is a fast and numerically stable for linear system solving, inversion, and factorization compared to singular valued decomposition (SVD), QR factorization and LU decomposition. As different methods exist to find the Cholesky decomposition of a given matrix. This paper presents the comparative study of a proposed RChol algorithm with the conventional methods. The RChol algorithm is an explicit way to estimate the modified Cholesky factors of a dynamic correlation matrix.