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92nd Annual Meeting of the International Association of applied Mathematics and Mechanics, gamm 2022

作者： Alqahtani, Abdulaziz Mach, Thomas Reic Hel, Lothar Department of Mathematics King Khalid University P.O. Box 9004 Abha Saudi Arabia Institute for Mathematics University of Potsdam Potsdam14476 Germany Department of Mathematical Sciences Kent State University KentOH44242 United States

linear ill-posed problems often are analyzed in function spaces using tools from functional analysis, while their numerical solution typically is computed by first discretizing the problem and then applying tools from finite-dimensional linear algebra. The Chebfun package makes it possible to solve linear ill-posed problems without explicit discretization. This work discusses the use of Tikhonov regularization with a fairly general linear regularization operator within the Chebfun framework. © 2023 The Authors.

关键词： linear algebra

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Solving Different numerical linear algebra Problems with a New General Fast Neurodynamics

Solving Different Numerical Linear Algebra Problems with a N...

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International workshop on Advanced Computational Intelligence (IWACI)

作者： Dimitrios Gerontitis Panagiotis Tzekis Yang Shi Dept. of Information and Electronic Engineering International Hellenic University Thessaloniki Greece School of Information Engineering Yangzhou University Yangzhou China

ISBN: (数字)9798350308501

ISBN: (纸本)9798350308518

The scientific research on issues related to numerical linear algebra constitutes an interesting topic for study in the last decades. In this manuscript, a general and fast recurrent neural network (RNN) model based on an extended activation function (AF) will be designed and applied for the solution of different numerical linear algebra problems. Theoretical convergence analysis and simulation examples, in simulink will show the efficiency and the accelerated convergence ability of the new dynamical system.

关键词： Neurodynamics Recurrent neural networks Tensors Mathematical models Vectors Trajectory Manipulator dynamics

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gamm Annual Meeting – Kassel 2020 Overview of the Sections

GAMM Annual Meeting – Kassel 2020 Overview of the Sections

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Volume 20 (2020), Issue 1 of PAMM "Proceedings in applied Mathematics and Mechanics" assembles the contributions to the 91st Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (gamm), organized in 2020 by Universität Kassel, Germany, and held as a virtual conference. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections. gamm related DFG Priority Programmes. DFG-PP 1748 Reliable Simulation Techniques in Solid Mechanics. Development of Non-Standard Discretization Methods, Mechanical and Mathematical Analysis. DFG-PP 1881 Turbulent Superstructure. DFG-PP 1886 Polymorphic Uncertainty Modelling for the numerical Design of Structures. DFG-PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation. DFG-PP 2020 Cyclic Deterioration of High-Performance Concrete in an Experimental-Virtual Lab. Minisymposia. MS 1 Computational Photonics. MS 3 Dissipativity, turnpikes and optimal control. MS 4 Advanced experimental and computational techniques in polymer mechanics. Sections 1–24. S1 Multi-body dynamics. S2 Biomechanics. S3 Damage and fracture mechanics. S4 Structural mechanics. S5 Nonlinear oscillations. S6 Material modelling in solid mechanics. S7 Coupled problems. S8 Multiscales and homogenization. S9 Laminar flows and transition. S10 Turbulence and reactive flows. S11 Interfacial flows. S12 Waves and acoustics. S13 Flow control. S14 applied analysis. S15 Uncertainty quantification. S16 Optimization. S17 applied and numerical linear algebra. S18 numerical methods of differential equations. S19 Optimization of differential equations. S20 Dynamics and control. S21 Mathematical signal and image processing. S22 Scientific computing. S24 History of mechanics. Young Researchers' Minisymposia. YRM1 Algorithms for coupled multi-physics problems. YRM2 Rank structured matrix and tensor techniques. YRM6 Novel discretization methods for

关键词： Fracture mechanics

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Topical Issue applied and numerical linear algebra (2/2)

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gamm Mitteilungen 2020年第4期43卷

作者： Güttel, Stefan Liesen, Jörg Manchester United Kingdom Berlin Germany

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gamm Annual Meeting Aachen 2022 Overview of the Sections

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PAMM 2023年第1期22卷

Volume 22 (2022), Issue 1 of PAMM “Proceedings in applied Mathematics and Mechanics” assembles the contributions to the 92nd Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (gamm), organized in 2022 by RWTH Aachen University. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections gamm related DFG Priority Programmes DFG-PP 1886 Polymorphic Uncertainty Modelling for the numerical Design of Structures DFG-PP 2013 The utilization of residual stresses induced by metal forming DFG-PP 2020 Cyclic Deterioration of High-Performance Concrete in an Experimental-Virtual Lab DFG-PP 2256 Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials Minisymposia MS 1 Mechanics of Foams MS 4 Evolution Equations with Gradient Flow Structure Sections 1–26 S1 Multi-body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 applied analysis S15 Uncertainty quantification S16 Shape Optimization S17 applied and numerical linear algebra S18 numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S24 History of mathematics S25 Computational and mathematical methods in data science S26 Modelling, analysis and simulation of molecular systems Young Researchers' Minisymposia YR3 Dynamic inversion and control of mechanical underactuated systems YR4 Computational design optimization

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gamm Annual Meeting – Kassel 2020 Overview of the Sections

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PAMM 2021年第1期20卷

Volume 20 (2020), Issue 1 of PAMM “Proceedings in applied Mathematics and Mechanics” assembles the contributions to the 91st Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (gamm), organized in 2020 by Universität Kassel, Germany, and held as a virtual conference. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections gamm related DFG Priority Programmes DFG-PP 1748 Reliable Simulation Techniques in Solid Mechanics. Development of Non-Standard Discretization Methods, Mechanical and Mathematical Analysis DFG-PP 1881 Turbulent Superstructure DFG-PP 1886 Polymorphic Uncertainty Modelling for the numerical Design of Structures DFG-PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation DFG-PP 2020 Cyclic Deterioration of High-Performance Concrete in an Experimental-Virtual Lab Minisymposia MS 1 Computational Photonics MS 3 Dissipativity, turnpikes and optimal control MS 4 Advanced experimental and computational techniques in polymer mechanics Sections 1–24 S1 Multi-body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S9 Laminar flows and transition S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 applied analysis S15 Uncertainty quantification S16 Optimization S17 applied and numerical linear algebra S18 numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S24 History of mechanics Young Researchers' Minisymposia YRM1 Algorithms for coupled multi-physics problems YRM2 Rank structured matrix and tensor techniques YRM6 Novel discretization methods for phase-field modeling in fracture mecha

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gamm Annual Meeting – Kassel 2021 Overview of the Sections

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PAMM 2021年第1期21卷

Volume 21 (2021), Issue 1 of PAMM “Proceedings in applied Mathematics and Mechanics” assembles the contributions to the 92nd Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (gamm), organized in 2021 by Universität Kassel, Germany, and held as a virtual conference. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections gamm related DFG Priority Programmes DFG-PP 1886 Polymorphic Uncertainty Modelling for the numerical Design of Structures DFG-PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation DFG-PP 2020 Cyclic Deterioration of High-Performance Concrete in an Experimental-Virtual Lab DFG-PP 2256 Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials Minisymposia MS 1 Computational Photonics MS 2 Symbolic computation methods for differential equations, dynamical systems, and control theory MS 4 Advanced experimental and computational techniques in polymer mechanics Sections 1–24 S1 Multi-body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S9 Laminar flows and transition S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 applied analysis S15 Uncertainty quantification S16 Optimization S17 applied and numerical linear algebra S18 numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S24 History of mechanics Young Researchers' Minisymposia YRM1 Algorithms for coupled multi-physics problems YRM3 Recent developments in isogeometric analysis for flow problemes YRM6 Novel discretization methods for phase-field modeling in fracture mechanics

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gamm Annual Meeting – Vienna 2019 Overview of the Sections

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PAMM 2019年第1期19卷

Volume 19 (2019) of PAMM “Proceedings in applied Mathematics and Mechanics” assembles the contributions to the 90 th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (gamm), organized on February 18–22, 2019 by Technische Universität Wien, Austria. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections gamm related DFG Priority Programmes DFG–PP 1748 Reliable Simulation Techniques in Solid Mechanics. Development of Non–Standard Discretization Methods, Mechanical and Mathematical Analysis DFG–PP 1886 Polymorphic Uncertainty Modelling for the numerical Design of Structures DFG–PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation DFG–PP 2020 Cyclic Deterioration of High–Performance Concrete in an Experimental–Virtual Lab Minisymposia MS 1 Mathematical modeling, analysis and simulation of drug distribution for efficient pharmacotherapy MS 2 Topology optimization of structures considering elaborate constraints and variables MS 3 Research software and –data: How to ensure replicability, reproducibility, and reusability MS 4 Coupled problems in rotating machinery Sections 1–24 S1 Multi-body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S9 Laminar flows and transition S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 applied analysis S15 Uncertainty quantification S16 Optimization S17 applied and numerical linear algebra S18 numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S23 applied operator theory S24 History of fluid mechanics and history, teaching and popularization of mathemati

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Multistep matrix splitting iteration preconditioning for singular linear systems

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numerical ALGORITHMS 2017年第2期75卷 457-475页

作者： Morikuni, Keiichi Univ Tsukuba Fac Engn Informat & Syst Div Informat Engn 1-1-1 Tennodai Tsukuba Ibaraki 3058573 Japan

Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES) method. We present theoretical and practical justifications for using this approach. numerical experiments show that the multistep generalized shifted splitting (GSS) and Hermitian and skew-Hermitian splitting (HSS) iteration preconditioning are more robust and efficient compared to standard preconditioners for some test problems of large sparse singular linear systems.

关键词： Preconditioning Inner-outer iteration GMRES method Flexible GMRES method Matrix splitting iterations Singular linear system

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On the computation of a truncated SVD of a large linear discrete ill-posed problem

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numerical ALGORITHMS 2017年第2期75卷 359-380页

作者： Onunwor, Enyinda Reichel, Lothar Kent State Univ Dept Math Sci Kent OH 44242 USA Stark State Coll Dept Math 6200 Frank Ave NW North Canton OH 44720 USA

The singular value decomposition is commonly used to solve linear discrete ill-posed problems of small to moderate size. This decomposition not only can be applied to determine an approximate solution but also provides insight into properties of the problem. However, large-scale problems generally are not solved with the aid of the singular value decomposition, because its computation is considered too expensive. This paper shows that a truncated singular value decomposition, made up of a few of the largest singular values and associated right and left singular vectors, of the matrix of a large-scale linear discrete ill-posed problems can be computed quite inexpensively by an implicitly restarted Golub-Kahan bidiagonalization method. Similarly, for large symmetric discrete ill-posed problems a truncated eigendecomposition can be computed inexpensively by an implicitly restarted symmetric Lanczos method.

关键词： Discrete ill-posed problem Truncated SVD Lanczos method Golub-Kahan bidiagonalization

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