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Numerical Continuation Methods
Backward Error Analysis and Structure Preservation
other
Author(s):
Ernst Hairer
,
Gerhard Wanner
,
Christian Lubich
Publication date
(Print):
2002
Publisher:
Springer Berlin Heidelberg
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Core Readings in Statistical Mediation Analysis
Author and book information
Book Chapter
Publication date (Print):
2002
Pages
: 287-326
DOI:
10.1007/978-3-662-05018-7_9
SO-VID:
6a793b3a-50d9-4b63-b554-15b74f139e71
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Book chapters
pp. 1
The Standard Galerkin Method
pp. 1
Introduction
pp. 1
Stochastic programming, an Introduction
pp. 1
Examples and Numerical Experiments
pp. 7
The Basic Principles of Continuation Methods
pp. 17
Newton’s Method as Corrector
pp. 23
Methods Based on More General Approximations of the Elliptic Problem
pp. 23
Numerical Integrators
pp. 28
Solving the Linear Systems
pp. 33
Approximation Techniques in Stochastic Programming
pp. 35
Nonsmooth Data Error Estimates
pp. 37
Convergence of Euler-Newton-Like Methods
pp. 44
Steplength Adaptations for the Predictor
pp. 47
Order Conditions, Trees and B-Series
pp. 51
More General Parabolic Equations
pp. 61
Predictor-Corrector Methods Using Updating
pp. 63
Maximum-Norm Stability and Error Estimates
pp. 65
Large Scale Linear Programming Techniques
pp. 75
Detection of Bifurcation Points Along a Curve
pp. 81
Negative Norm Estimates and Superconvergence
pp. 91
Calculating Special Points of the Solution Curve
pp. 93
Conservation of First Integrals and Methods on Manifolds
pp. 95
Nonlinear Programming Techniques Applied to Stochastic Programs with Recourse
pp. 95
Single Step Fully Discrete Schemes for the Homogeneous Equation
pp. 96
Large Scale Problems
pp. 111
Single Step Methods and Rational Approximations of Semigroups
pp. 112
Numerically Implementable Existence Proofs
pp. 123
Numerical Solution of Probabilistic Constrained Programming Problems
pp. 127
Single Step Fully Discrete Schemes for the Inhomogeneous Equation
pp. 131
Symmetric Integration and Reversibility
pp. 141
Stochastic Quasigradient Methods
pp. 145
Multistep Backward Difference Methods
pp. 151
PL Continuation Methods
pp. 163
Incomplete Iterative Solution of the Algebraic Systems at the Time Levels
pp. 167
Symplectic Integration of Hamiltonian Systems
pp. 173
PL Homotopy Algorithms
pp. 181
The Discontinuous Galerkin Time Stepping Method
pp. 183
Boundary Element Methods
pp. 187
Multidimensional Integration and Stochastic Programming
pp. 201
Stochastic Integer Programming
pp. 203
General PL Algorithms on PL Manifolds
pp. 209
Further Topics in Structure Preservation
pp. 209
A Nonlinear Problem
pp. 215
A Proposed Standard Input Format for Computer Codes which Solve Stochastic Programs with Recourse
pp. 223
Semilinear Parabolic Equations
pp. 229
A Computer Code for Solution of Probabilistic-Constrained Stochastic Programming Problems
pp. 233
Approximating Implicitly Defined Manifolds
pp. 237
Conditional Probability and Conditional Expectation of a Random Vector
pp. 239
The Method of Lumped Masses
pp. 252
Update Methods and their Numerical Stability
pp. 253
The H1 and H-1 Methods
pp. 255
Structure-Preserving Implementation
pp. 255
An L-Shaped Method Computer Code for Multi-Stage Stochastic Linear Programs
pp. 267
The Relationship between the L-Shaped Method and Dual Basis Factorization for Stochastic Linear Programming
pp. 267
A Mixed Method
pp. 273
Design and Implementation of a Stochastic Programming Optimizer with Recourse and Tenders
pp. 279
A Singular Problem
pp. 287
Backward Error Analysis and Structure Preservation
pp. 295
An Implementation of the Lagrangian Finite-Generation Method
pp. 313
Stochastic Quasigradient Methods and their Implementation
pp. 327
Hamiltonian Perturbation Theory and Symplectic Integrators
pp. 353
Stepsize Rules, Stopping Times and their Implementation in Stochastic Quasigradient Algorithms
pp. 373
Adaptive Stochastic Quasigradient Procedures
pp. 375
Reversible Perturbation Theory and Symmetric Integrators
pp. 385
A Note About Peojections in the Implementation of Stochastic Quasigradient Methods
pp. 391
Dissipatively Perturbed Hamiltonian and Reversible Systems
pp. 393
Descent Stochastic Quasigdadient Methods
pp. 403
Stochastic Integer Programming by Dynamic Programming
pp. 407
Highly Oscillatory Differential Equations
pp. 413
Facility Location Problem
pp. 435
Lake Eutrophication Management: The Lake Balaton Project
pp. 445
Optimal Investments for Electricity Generation: A Stochastic Model and a Test-Problem
pp. 455
Some Applications of Stochastic Optimization Methods to the Electric Power System
pp. 455
Dynamics of Multistep Methods
pp. 465
Power Generation Planning with Uncertain Demand
pp. 481
Exhaustible Resource Models with Uncertain Returns from Exploration Investment
pp. 489
A Two-Stage Stochastic Facility-Location Problem with Time-Dependent Supply
pp. 515
Some Test Problems for Stochastic Nonlinear Multistage Programs
pp. 543
Stochastic Programming Problems: Examples from the Literature
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