Publications related to Rational function

Efficient Continual Finite-Sum Minimization

Volkan Cevher, Efstratios Panteleimon Skoulakis, Leello Tadesse Dadi

Given a sequence of functions

f_1,\ldots,f_n

with

f_i:\mathcal{D}\mapsto \mathbb{R}

, finite-sum minimization seeks a point

{x}^\star \in \mathcal{D}

minimizing

\sum_{j=1}^nf_j(x)/n

. In this work, we propose a key twist into the finite-sum minimizat ...

2024

Ultra long turbulent eddies, magnetic topology, and the triggering of internal transport barriers in tokamaks

Stephan Brunner, Justin Richard Ball, Arnas Volcokas

Local nonlinear gyrokinetic simulations of tokamak plasmas demonstrate that turbulent eddies can extend along magnetic field lines for hundreds of poloidal turns when the magnetic shear is very small. By accurately modeling different field line topologies ...

IOP Publishing Ltd2023

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Andreas Loukas, Nikolaos Karalias

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

Rational-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

Francesca Bonizzoni, Davide Pradovera

We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite el ...

2021

Functional Tucker Approximation Using Chebyshev Interpolation

Daniel Kressner, Christoph Max Strössner

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

SIAM PUBLICATIONS2021

Frequency-Domain Non-intrusive Greedy Model Order Reduction Based on Minimal Rational Approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

On Proving and Disproving Equivalence of Functional Programming Assignments

Viktor Kuncak, Dragana Milovancevic

We present an automated approach for verifying the correctness of programming assignments, such as ones arising in a functional programming course. Our approach takes a small set of reference implementations and a set of student implementations and checks, ...

2021

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

MATHICSE2020

Rational function

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Efficient Continual Finite-Sum Minimization

Ultra long turbulent eddies, magnetic topology, and the triggering of internal transport barriers in tokamaks

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Rational-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

Functional Tucker Approximation Using Chebyshev Interpolation

Frequency-Domain Non-intrusive Greedy Model Order Reduction Based on Minimal Rational Approximation

On Proving and Disproving Equivalence of Functional Programming Assignments

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

Functional Tucker Approximation Using Chebyshev Interpolation

Efficient Continual Finite-Sum Minimization

Rational-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

MATHICSE Technical Report : Frequency-domain non-intrusive greedy Model Order Reduction based on minimal rational approximation

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Ultra long turbulent eddies, magnetic topology, and the triggering of internal transport barriers in tokamaks

On Proving and Disproving Equivalence of Functional Programming Assignments

Frequency-Domain Non-intrusive Greedy Model Order Reduction Based on Minimal Rational Approximation

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast