# Factorization of Saddle-point Matrices in Dynamical Systems Optimization---Reusing Pivots

## TL;DR

This paper introduces a method for efficiently solving sequences of saddle-point systems in dynamical systems optimization by reusing pivots in LDL^T factorizations, leading to faster computations.

## Contribution

The paper presents a novel approach to reuse pivots in LDL^T factorizations for saddle-point matrices, improving computational efficiency in dynamical systems optimization.

## Key findings

- Method outperforms Bunch-Parlett in speed
- Reuses pivots to reduce computation time
- Maintains same accuracy as traditional methods

## Abstract

In this paper we consider the application of direct methods for solving a sequence of saddle-point systems. Our goal is to design a method that reuses information from one factorization and applies it to the next one. In more detail, when we compute the pivoted $LDL^T$ factorization we speed up computation by reusing already computed pivots and permutations. We develop our method in the frame of dynamical systems optimization. Experiments show that the method improves efficiency over Bunch-Parlett while delivering the same results.