Generalized minimal residual method

Formal sciences
Mathematics
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Numerical analysis

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Novel corrector problems with exponential decay of the resonance error for numerical homogenization

Edoardo Paganoni

Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...

EPFL2020

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

Daniel Kressner, Stefano Massei, Kathryn Dianne Lund

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

2020

Random extrapolation for primal-dual coordinate descent

Volkan Cevher, Ahmet Alacaoglu

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, an ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2020

Smooth Power Direction Transition of a Bidirectional LLC Resonant Converter for DC Transformer Applications

Drazen Dujic, Jakub Kucka

The bidirectional LLC resonant converter operated at fixed switching frequency is a preferable candidate for a true dc transformer that does not actively control the power flow. This is due to its naturally stiff voltage ratio regardless of the imposed loa ...

2020

Exact Diffusion for Distributed Optimization and Learning-Part I: Algorithm Development

Ali H. Sayed, Bicheng Ying, Kun Yuan

This paper develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II of this paper to have a wider stability range an ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Daniel Kressner, Zvonimir Bujanovic

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...

SIAM PUBLICATIONS2018

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

Recompression Of Hadamard Products Of Tensors In Tucker Format

Daniel Kressner, Lana Perisa

The Hadamard product features prominently in tensor-based algorithms in scientific computing and data analysis. Due to its tendency to significantly increase ranks, the Hadamard product can represent a major computational obstacle in algorithms based on lo ...

Siam Publications2017

A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics

Alfio Quarteroni, Andrea Manzoni

When relying on Newton iterations to solve nonlinear problems in the context of Reduced Basis (RB) methods, the assembling of the RB arrays during the online stage depends on the dimension of the underlying high-fidelity approximation. This is more of an i ...

Elsevier Science Sa2017

Frank-Wolfe Works for Non-Lipschitz Continuous Gradient Objectives: Scalable Poisson Phase Retrieval

Volkan Cevher, Quoc Tran Dinh, Alp Yurtsever, Yen-Huan Li, Ya-Ping Hsieh, Marwa El Halabi, Gergely Odor

We study a phase retrieval problem in the Poisson noise model. Motivated by the PhaseLift approach, we approximate the maximum-likelihood estimator by solving a convex program with a nuclear norm constraint. While the Frank-Wolfe algorithm, together with t ...

Ieee2016

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