Computation of invariant measures with dimension reduction methods

By (author) Jens Kemper

Extent: 158 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: English

Paperback (Published)

(April 2010)

ISBN: 9783832524524

5.71 x 8.27 inches

Price: $56.00

Out of stock

Add to cart -
back order

Synopsis
Contributing Authors

In recent years, Dellnitz, Junge and co-workers developed a subdivision algorithm for the approximation of invariant measures in discrete dynamical systems based on the so-called Ulam’s approach. In high dimensions, this adaptive invariant measure (AIM) algorithm suffers from the “curse of dimension” even when the support of the system’s invariant measure is known to be low-dimensional. In our thesis we develop algorithms facing this problem by combining the subdivision technique with proper orthogonal decomposition (POD) as a model reduction method. We derive explicit error bounds concerning the long-time behavior of POD solutions, propose a discrete version of the Prohorov metric as a proper distance notion for discrete measures computed by the algorithms, and analytically compare the approximation processes of the AIM algorithm and the POD-based algorithms. A marginal-like representation of discrete measures is proposed in order to visualize the numerical experiments. The algorithms are applied to finite element discretizations of the Chafee-Infante problem in order to show the power of our approach.

By (author) Jens Kemper

Similar Books

The New Other

Alien Intelligence and the Innovation Drive

By (author) Amy Levy

Transitive Media [Philosophy]

Think(er)ing Technologies in Real-Time

By (author) Wolfgang Ernst

Care in an Era of New Technologies and Artificial Intelligence

Relationships in a Connected World

Volume 14

By (author) V. Nurock

City in the Cloud – Data on the Ground

The Architecture of Data

Edited by Damjan Kokalevski Edited by Andres Lepik Edited by Cara Hähl-Pfeifer Contributions by James…

Global Histories of Video Game Music Technology

Volume 8

Edited by Karen M. Cook Edited by William Bibbons Edited by Fanny Rebillard

Natural Resources in Early Modern Economies of Knowledge

Volume 40

edited by Pietro Daniel Omodeo and Helge Wendt

Physical Characterization of Coatings

Introduction to Rheology and Surface Analysis

By (author) Michael Osterhold

The Physics of the Mind

New Perspectives for Psychotherapists, Healers and Seekers

By (author) Phil Mollon

Buchblogs zwischen Passion und Profession

Zur Diskursivierung digitaler literaturbezogener Anschlusskommunikation als Arbeit

Volume 5

by Kristina Petzold

Falschung, Betrug, Beliebigkeit

der Vertrauensverlust der Wissenschaft

by Manfred Velden

Articulations of the Nuclear

Postwar Japan under the Spell of the Atomic Age

Volume 13

edited by Stephan Kohn and Katharina Hulsmann

Artificial Morality

An Exploration of Moral Machines

Volume 4

by Andrei Nutas

Decameter Radio Emission of the Sun

edited by Valentin Nikolayevich Melnik and Helmut O. Rucker

Development of a telemetry system for monitoring piston characteristics inside combustion engines

By (author) Paul Lagaly

Global History of Techniques

(19th-21st Centuries)

Volume 9

Edited by Guillaume Carnino Edited by Liliane Hilaire-Perez Edited by Jerome Lamy

Language, Technology, Humanities in Society 5.0

Edited by Maria Banaś Edited by Grzegorz Wlaźlak

Numbers, Measures, and the Transfer of Goods in Prehistory

Volume 6

Edited by Philippe Della Casa Edited by Aleksander Dzbyński

On the Scattering Behavior of Dielectric Corner Reflectors in Distributed Radar Systems

By (author) Christian Alexander Buchberger

Proceedings of the 7th Symposium of the Hellenic Society for Archaeometry

Archaeology Archaeometry: 30 Years Later

Edited by Eleni Filippaki

RNA Made Simple

The Essential Guide to Extraction

By (author) Christian Siadjeu By (author) Dirk C Albach

Route and Operating Optimization of Maritime Vessels Using Machine Learning Techniques

By (author) Mohammad Hossein Moradi

Short-Term Load Forecasting using Machine Learning Methods

Volume 7

By (author) Sylwia Henselmeyer

Sovereign by Design

The LIONS Approach to Digital Sovereignty

Edited by Isabelle Fries Edited by Michael Grabatin Edited by Manfred Hofmeier

The Promise and Peril of AI and IA

New Technology Meets Religion, Theology, and Ethics

edited by Ted Peters

Die unsichtbare Welt

Beitrage zur Weltwahrnehmung in den Wissenschaften

edited by Klaus Bohmer, Paul-Gerhard Reinhard and Dirk Evers

A Cultural History of Silicon Valley

Volume 325

By (author) Neslihan Bulut

Die Einfuhrung ins richtige Handeln in der Arithmetik (Madhal ar-rasad ila ‘ilm al-‘adad) von al-Qalasadi (st. 1486)

Bearbeitung und Einordnung in die magribinische Mathematikgeschichte

Volume 19

by Ulrich Rebstock

I disegni e i discorsi di Giovanni Antonio Nigrone vol. I

fontanaro e ingegniero de acqua (1585-1609 ca.)

Volume 481

by Gaia Bruno

I disegni e i discorsi di Giovanni Antonio Nigrone vol. II

Fontanaro e ingegniero de acqua (1585-1609 ca.)

Volume 497

edited by Gaia Bruno and David Gentilcore

Ingenieurs mais apprentis

Volume 32

by Arnaud Pierrel

Analysing Data from Capacitive Floor Sensors for Human Gait Assessment Using Artificial Neural Networks

Volume 5

By (author) Raoul Hoffmann

Annual Report 2022

Laboratory of Ion Beam Physics

By (author) LIBRUM Publishers & Editors

Building and Designing Transistor Radios

A Beginner's Guide

by R H Warring

Building and Designing Transistor Radios

A Beginner's Guide

by R H Warring

Contributions to Model Predictive Active Vibration Control under Parametric Resonance

Volume 24

By (author) Joe Ismail

Learning with Light and Shadows

Educational Lantern and Film Projection, 1860-1990

Volume 8

Edited by Nelleke Teughels Edited by Kaat Wils

Modeling Methods for Process Induced Distortions of CFRP-Parts produced in the Prepreg-Autoclave-Process

Volume 20

By (author) Tim Frerich

Non-Intrusive Methodologies for Large Area Urban Research

Edited by Ian Haynes Edited by Thea Ravasi Edited by Stephen Kay Edited by Salvatore…

Performance Management in Humanitarian Logistics

Development of a Process-driven and IT-supported Performance Measurement System

Volume 66

By (author) Adam Widera

Real-Time Auralisation of Outdoor Sound Propagation

Volume 39

By (author) Jonas Stienen

Supporting Operational and Real-time Planning Tasks of Road Freight Transport with Machine Learning

Guiding the Implementation of Machine Learning Algorithms

Volume 69

By (author) Sandra Lechtenberg

World War Two Simulated

Digital Games and Reconfigurations of the Past

by Curtis D. Carbonell

Computation of invariant measures with dimension reduction methods

Tell a Colleague/Librarian/Friend

Similar Books

Join the ISD Mailing List