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Concept

Steffensen's method

Related publications (5)

Approximating dynamic equilibrium conditions with macroscopic fundamental diagrams

Nikolaos Geroliminis, Mehmet Yildirimoglu

Real-time coordinated traffic management strategies that benefit from parsimonious models with aggregated network dynamics, provide a new generation of smart hierarchical strategies to improve network capacity and performance. However, this raises the ques ...

Elsevier2014

A higher-order numerical framework for stochastic simulation of chemical reaction systems

Background: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulatio ...

Biomed Central Ltd2012

A multi-iterate method to solve systems of nonlinear equations

Michel Bierlaire, Michaël Clément Louis Ghislain Thémans, Frank Crittin

We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propo ...

2007

Numerical methods and models relevant to transportation applications

Michaël Clément Louis Ghislain Thémans

In this thesis, we focus on standard classes of problems in numerical optimization: unconstrained nonlinear optimization as well as systems of nonlinear equations. More precisely, we consider two types of unconstrained nonlinear optimization problems. On t ...

EPFL2007

Solving noisy large scale fixed point problems and systems of nonlinear equations

Michel Bierlaire, Frank Crittin

Many complex transportation models can be formulated as fixed-point problems. Typical examples are the equilibrium-like models, motivated by the need to capture the interaction between the transport supply (that is, the infrastructure) and transport demand ...

2006