Inertia-preserving secant updates

Direct Secant Updates of Matrix Factorizations

This paper presents a new context for using the sparse Broyden update method to solve systems of nonlinear equations. The setting for this work is that a Newton-like algorithm is assumed to be available which incorporates a workable strategy for improving poor initial guesses and providing a satisfactory Jacobian matrix approximation whenever required. The total cost of obtaining each Jacobian ...

Quasi-Newton updates with weighted secant equations

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

A Curvilinear Search Using Tridiagonal Secant Updates for Unconstrained Optimization

Most General Property-Preserving Updates

Most General Property-Preserving Updates (TR)

Systems need to be updated to last for a long time in a dynamic environment, and to cope with changing requirements. It is important for updates to preserve the desirable properties of the system under update, while possibly enforcing new ones. Here we consider a simple yet general update mechanism, which replaces a component of the system with a new one. The context, i.e., the rest of the syst...