Numerische Mathematik最新文献_第6页

A unifying framework for tangential interpolation of structured bilinear control systems 结构双线性控制系统切向插补的统一框架

2区数学

Numerische Mathematik Pub Date : 2023-10-31 DOI: 10.1007/s00211-023-01380-w

Peter Benner, Serkan Gugercin, Steffen W. R. Werner

引用次数: 2

On generating Sobolev orthogonal polynomials 关于索博列夫正交多项式的生成

2区数学

Numerische Mathematik Pub Date : 2023-10-31 DOI: 10.1007/s00211-023-01379-3

Niel Van Buggenhout

引用次数: 0

Grid-free weighted particle method applied to the Vlasov–Poisson equation 无网格加权粒子法在Vlasov-Poisson方程中的应用

2区数学

Numerische Mathematik Pub Date : 2023-10-26 DOI: 10.1007/s00211-023-01378-4

Yoann Le Henaff

引用次数: 0

Statistical properties of BayesCG under the Krylov prior Krylov先验下BayesCG的统计性质

2区数学

Numerische Mathematik Pub Date : 2023-10-12 DOI: 10.1007/s00211-023-01375-7

Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne, Chris J. Oates

引用次数: 0

Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods 用迹估计量和有理Krylov方法计算大矩阵的von Neumann熵

2区数学

Numerische Mathematik Pub Date : 2023-09-28 DOI: 10.1007/s00211-023-01368-6

Michele Benzi, Michele Rinelli, Igor Simunec

{"title":"Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods","authors":"Michele Benzi, Michele Rinelli, Igor Simunec","doi":"10.1007/s00211-023-01368-6","DOIUrl":"https://doi.org/10.1007/s00211-023-01368-6","url":null,"abstract":"Abstract We consider the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix A , defined as $${{,textrm{tr},}}(f(A))$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow> <mml:mspace /> <mml:mtext>tr</mml:mtext> <mml:mspace /> </mml:mrow> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>A</mml:mi> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> where $$f(x)=-xlog x$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mi>x</mml:mi> <mml:mo>log</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:math> . After establishing some useful properties of this matrix function, we consider the use of both polynomial and rational Krylov subspace algorithms within two types of approximations methods, namely, randomized trace estimators and probing techniques based on graph colorings. We develop error bounds and heuristics which are employed in the implementation of the algorithms. Numerical experiments on density matrices of different types of networks illustrate the performance of the methods.","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135386246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Improved ParaDiag via low-rank updates and interpolation 通过低秩更新和插值改进了ParaDiag

2区数学

Numerische Mathematik Pub Date : 2023-09-20 DOI: 10.1007/s00211-023-01372-w

Daniel Kressner, Stefano Massei, Junli Zhu

引用次数: 0

Analysis and approximations of an optimal control problem for the Allen–Cahn equation Allen-Cahn方程最优控制问题的分析与逼近

2区数学

Numerische Mathematik Pub Date : 2023-09-20 DOI: 10.1007/s00211-023-01374-8

Konstantinos Chrysafinos, Dimitra Plaka

引用次数: 0

Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems 基于算子分裂的线性微分-代数port- hamilton系统动态迭代

2区数学

Numerische Mathematik Pub Date : 2023-09-20 DOI: 10.1007/s00211-023-01369-5

Andreas Bartel, Michael Günther, Birgit Jacob, Timo Reis

引用次数: 3

Analysis of the single reference coupled cluster method for electronic structure calculations: the full-coupled cluster equations 电子结构计算的单参考耦合簇法分析:全耦合簇方程

2区数学

Numerische Mathematik Pub Date : 2023-09-13 DOI: 10.1007/s00211-023-01371-x

Hassan, Muhammad, Maday, Yvon, Wang, Yipeng

{"title":"Analysis of the single reference coupled cluster method for electronic structure calculations: the full-coupled cluster equations","authors":"Hassan, Muhammad, Maday, Yvon, Wang, Yipeng","doi":"10.1007/s00211-023-01371-x","DOIUrl":"https://doi.org/10.1007/s00211-023-01371-x","url":null,"abstract":"Abstract The central problem in electronic structure theory is the computation of the eigenvalues of the electronic Hamiltonian—a semi-unbounded, self-adjoint operator acting on an $$L^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -type Hilbert space of antisymmetric functions. Coupled cluster (CC) methods, which are based on a non-linear parameterisation of the sought-after eigenfunction and result in non-linear systems of equations, are the method of choice for high-accuracy quantum chemical simulations. The existing numerical analysis of coupled cluster methods relies on a local, strong monotonicity property of the CC function that is valid only in a perturbative regime, i.e., when the sought-after ground state CC solution is sufficiently close to zero. In this article, we introduce a new well-posedness analysis for the single reference coupled cluster method based on the invertibility of the CC derivative. Under the minimal assumption that the sought-after eigenfunction is intermediately normalisable and the associated eigenvalue is isolated and non-degenerate, we prove that the continuous (infinite-dimensional) CC equations are always locally well-posed. Under the same minimal assumptions and provided that the discretisation is fine enough, we prove that the discrete Full-CC equations are locally well-posed, and we derive residual-based error estimates with guaranteed positive constants. Preliminary numerical experiments indicate that the constants that appear in our estimates are a significant improvement over those obtained from the local monotonicity approach.","PeriodicalId":49733,"journal":{"name":"Numerische Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134989487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Interpolation operators for parabolic problems 抛物型问题的插值算子

2区数学

Numerische Mathematik Pub Date : 2023-09-11 DOI: 10.1007/s00211-023-01373-9

Rob Stevenson, Johannes Storn

引用次数: 0