Springer Series in Computational Mathematics最新文献

英文中文

Numerical Methods for Fractional Differentiation 分数阶微分的数值方法

Springer Series in Computational Mathematics

Pub Date : 2019-10-15 DOI: 10.1007/978-981-15-0098-5

K. M. Owolabi, A. Atangana

引用次数: 68

Tensor Spaces and Numerical Tensor Calculus 张量空间与数值张量微积分

Springer Series in Computational Mathematics

Pub Date : 2012-02-24 DOI: 10.1007/978-3-642-28027-6

W. Hackbusch

引用次数: 515

Mixed and Hybrid Finite Element Methods 混合和混合有限元方法

Springer Series in Computational Mathematics

Pub Date : 2011-11-23 DOI: 10.1007/978-1-4612-3172-1

F. Brezzi, M. Fortin

引用次数: 4202

History of continued fractions and Pade approximants 连分式和帕德近似的历史

Springer Series in Computational Mathematics

Pub Date : 1990-12-20 DOI: 10.1007/978-3-642-58169-4

C. Brezinski

引用次数: 238

Numerical continuation methods - an introduction 数值延拓方法简介

Springer Series in Computational Mathematics

Pub Date : 1990-06-26 DOI: 10.2307/2153001

E. Allgower, K. Georg

1 Introduction.- 2 The Basic Principles of Continuation Methods.- 2.1 Implicitly Defined Curves.- 2.2 The Basic Concepts of PC Methods.- 2.3 The Basic Concepts of PL Methods.- 3 Newton's Method as Corrector.- 3.1 Motivation.- 3.2 The Moore-Penrose Inverse in a Special Case.- 3.3 A Newton's Step for Underdetermined Nonlinear Systems.- 3.4 Convergence Properties of Newton's Method.- 4 Solving the Linear Systems.- 4.1 Using a QR Decomposition.- 4.2 Givens Rotations for Obtaining a QR Decomposition.- 4.3 Error Analysis.- 4.4 Scaling of the Dependent Variables.- 4.5 Using LU Decompositions.- 5 Convergence of Euler-Newton-Like Methods.- 5.1 An Approximate Euler-Newton Method.- 5.2 A Convergence Theorem for PC Methods.- 6 Steplength Adaptations for the Predictor.- 6.1 Steplength Adaptation by Asymptotic Expansion.- 6.2 The Steplength Adaptation of Den Heijer & Rheinboldt.- 6.3 Steplength Strategies Involving Variable Order Predictors.- 7 Predictor-Corrector Methods Using Updating.- 7.1 Broyden's "Good" Update Formula.- 7.2 Broyden Updates Along a Curve.- 8 Detection of Bifurcation Points Along a Curve.- 8.1 Simple Bifurcation Points.- 8.2 Switching Branches Via Perturbation.- 8.3 Branching Off Via the Bifurcation Equation.- 9 Calculating Special Points of the Solution Curve.- 9.1 Introduction.- 9.2 Calculating Zero Points f(c(s)) = 0.- 9.3 Calculating Extremal Points minsf((c(s)).- 10 Large Scale Problems.- 10.1 Introduction.- 10.2 General Large Scale Solvers.- 10.3 Nonlinear Conjugate Gradient Methods as Correctors.- 11 Numerically Implementable Existence Proofs.- 11.1 Preliminary Remarks.- 11.2 An Example of an Implementable Existence Theorem.- 11.3 Several Implementations for Obtaining Brouwer Fixed Points.- 11.4 Global Newton and Global Homotopy Methods.- 11.5 Multiple Solutions.- 11.6 Polynomial Systems.- 11.7 Nonlinear Complementarity.- 11.8 Critical Points and Continuation Methods.- 12 PL Continuation Methods.- 12.1 Introduction.- 12.2 PL Approximations.- 12.3 A PL Algorithm for Tracing H(u) = 0.- 12.4 Numerical Implementation of a PL Continuation Algorithm.- 12.5 Integer Labeling.- 12.6 Truncation Errors.- 13 PL Homotopy Algorithms.- 13.1 Set-Valued Maps.- 13.2 Merrill's Restart Algorithm.- 13.3 Some Triangulations and their Implementations.- 13.4 The Homotopy Algorithm of Eaves & Saigal.- 13.5 Mixing PL and Newton Steps.- 13.6 Automatic Pivots for the Eaves-Saigal Algorithm.- 14 General PL Algorithms on PL Manifolds.- 14.1 PL Manifolds.- 14.2 Orientation and Index.- 14.3 Lemke's Algorithm for the Linear Complementarity Problem.- 14.4 Variable Dimension Algorithms.- 14.5 Exploiting Special Structure.- 15 Approximating Implicitly Defined Manifolds.- 15.1 Introduction.- 15.2 Newton's Method and Orthogonal Decompositions Revisited.- 15.3 The Moving Frame Algorithm.- 15.4 Approximating Manifolds by PL Methods.- 15.5 Approximation Estimates.- 16 Update Methods and their Numerical Stability.- 16.1 Introduction.- 16.2 Updates Using the Sherman-Morrison

1介绍。- 2延拓法的基本原理。- 2.1隐式定义曲线。- 2.2 PC方法的基本概念。- 2.3 PL方法的基本概念。- 3牛顿法作为校正。- 3.1动机。- 3.2特殊情况下的Moore-Penrose逆。- 3.3欠定非线性系统的牛顿步。- 3.4牛顿法的收敛性。- 4求解线性方程组。- 4.1使用QR分解。- 4.2给定旋转以获得QR分解。—4.3错误分析。- 4.4因变量的缩放。- 4.5使用LU分解。- 5类欧拉-牛顿方法的收敛性。- 5.1近似欧拉-牛顿法。- 5.2 PC方法的一个收敛定理。- 6步长调整预测器。- 6.1渐近展开的步长适应。- 6.2 Den Heijer & Rheinboldt的步长适应。- 6.3涉及可变顺序预测因子的步长策略。- 7使用更新的预测校正方法。- 7.1布罗登的“好”更新公式。- 7.2 Broyden沿着曲线更新。- 8分岔点沿曲线的检测。—8.1简单分叉点。- 8.2通过扰动切换支路。- 8.3通过分岔方程进行分支。- 9计算解曲线的特殊点。—9.1简介。- 9.2计算零点f(c(s)) = 0。- 9.3计算极值点minsf((c(s))。- 10个大规模问题。—10.1简介。- 10.2通用大规模求解器。- 10.3作为校正器的非线性共轭梯度法。- 11数值上可实现的存在性证明。—11.1初步备注。- 11.2一个可实现存在定理的例子。- 11.3获取浏览器定点的几种实现。11.4全局牛顿和全局同伦方法。—11.5多种解决方案。- 11.6多项式系统。- 11.7非线性互补。—11.8临界点和延续方法。- 12 PL延续方法。—12.1简介。- 12.2 PL近似。—12.3跟踪H(u) = 0的PL算法。- 12.4 PL延拓算法的数值实现。- 12.5整数标签。- 12.6截断错误。- 13 PL同伦算法。- 13.1集值映射。- 13.2美林的重启算法。13.3一些三角测量和它们的实现。- 13.4 Eaves & Saigal的同伦算法。- 13.5混合PL和牛顿阶梯。—13.6 Eaves-Saigal算法的自动枢轴。- 14 PL流形的一般PL算法。- 14.1 PL歧管。- 14.2方向和索引。- 14.3线性互补问题的Lemke算法。- 14.4变维算法。- 14.5利用特殊结构。- 15逼近隐式定义流形。- 15.1简介。- 15.2牛顿法和正交分解重述。- 15.3移动帧算法。- 15.4用PL方法逼近流形。- 15.5近似估计。- 16更新方法及其数值稳定性。- 16.1简介。—16.2使用Sherman-Morrison公式进行更新。- 16.3 QR分解。- 16.4 LU分解。- P1一个简单的PC延续方法。- P2 A PL同伦方法。- P3简单的欧拉-牛顿更新法。- P4处理分岔的连续算法。- P5 A PL表面发生器。- P6 SCOUT -简单延续工具。- P6.1简介。- P6.2计算算法。- P6.3交互式技术。—P6.4命令。示例:微分时滞方程的周期解。-索引和符号。

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引用次数: 1193

Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms Navier-Stokes方程的有限元方法。理论和算法

Springer Series in Computational Mathematics

Pub Date : 1986-06-19 DOI: 10.1007/978-3-642-61623-5

V. Girault, P. Raviart

引用次数: 4913

Newton-Type Approaches in Finite Dimension 有限维牛顿型方法

Springer Series in Computational Mathematics

Pub Date : 1900-01-01 DOI: 10.1007/978-981-13-7669-6_2

M. Nakao, M. Plum, Yoshitaka Watanabe

引用次数: 0

Multi-grid methods and applications 多网格方法和应用

Springer Series in Computational Mathematics

Pub Date : 1900-01-01 DOI: 10.1007/978-3-662-02427-0

W. Hackbusch

引用次数: 2648

Basic Principle of the Verification 核查的基本原则

Springer Series in Computational Mathematics

Pub Date : 1900-01-01 DOI: 10.1007/978-981-13-7669-6_1

M. Nakao, M. Plum, Yoshitaka Watanabe

引用次数: 0

Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations 偏微分方程的数值验证方法与计算机辅助证明

Springer Series in Computational Mathematics

Pub Date : 1900-01-01 DOI: 10.1007/978-981-13-7669-6

M. Nakao, M. Plum, Yoshitaka Watanabe

引用次数: 55

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