Concept

Biconjugate gradient method

Related publications (32)

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

MATHICSE2015

An Adjoint Approach for Stabilizing the Parareal Method

Jan Sickmann Hesthaven, Allan Svejstrup Nielsen, Yvon Maday

The parareal algorithm seeks to extract parallelism in the time-integration direction of time-dependent differential equations. While it has been applied with success to a wide range of problems, it suffers from some stability issues when applied to non-di ...

2015

MATHICSE Technical Report: Numerical homogenization methods for parabolic monotone problems

Assyr Abdulle

In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. ...

MATHICSE2015

Truncated low-rank methods for solving general linear matrix equations

Daniel Kressner, Petar Sirkovic

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

Wiley-Blackwell2015

Path-following gradient-based decomposition algorithms for separable convex optimization

Quoc Tran Dinh

A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require ...

Springer Verlag2014

A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations

Daniel Kressner, Christine Tobler

This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on a parameter. Specifically, we consider the situation when the parameter dependence is suffi ...

Wiley-Blackwell2013

Process Design and Optimization (MLS-S03): Model Identification by Gradient Methods

Julien Léo Billeter

This lecture describes the following topics: • Dynamic Models - Conservation of Mass (Concentration Measurements) - Conservation of Energy (Calorimetry) - Beer’s Law (Spectroscop ...

2013

Voltage Propagation Method for 3-D Power Grid Analysis

Giovanni De Micheli, Vasileios Pavlidis, Cheng Zhang

Power grid analysis is a challenging problem for mod- ern integrated circuits. For 3-D systems fabricated using stacked tiers with TSVs, traditional power grid analysis methods for pla- nar (2-D) circuits do not demonstrate the same performance. An efficie ...

2012

Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: A fully discrete spacetime analysis

Assyr Abdulle, Gilles Vilmart

Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge-Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following th ...

2012

Explicit methods for stiff stochastic differential equations

Assyr Abdulle

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...

Springer-Verlag Berlin2012

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.