Approximate Iterative Algorithms [Almudevar 2014-02-10].pdf

(2867 KB) Pobierz
Approximate Iterative Algorithms
Approximate Iterative Algorithms
Anthony Almudevar
Department of Biostatistics and Computational Biology,
University of Rochester, Rochester, NY, USA
CRC Press/Balkema is an imprint of the Taylor & Francis Group, an informa business
© 2014 Taylor & Francis Group, London, UK
Typeset by MPS Limited, Chennai, India
Printed and Bound by CPI Group (UK) Ltd, Croydon, CR0 4YY
All rights reserved. No part of this publication or the information contained
herein may be reproduced, stored in a retrieval system, or transmitted in any
form or by any means, electronic, mechanical, by photocopying, recording or
otherwise, without written prior permission from the publisher.
Although all care is taken to ensure integrity and the quality of this publication
and the information herein, no responsibility is assumed by the publishers nor
the author for any damage to the property or persons as a result of operation
or use of this publication and/or the information contained herein.
Library of Congress Cataloging-in-Publication Data
Almudevar, Anthony, author.
Approximate iterative algorithms / Anthony Almudevar, Department of
Biostatistics and Computational Biology, University of Rochester, Rochester, NY, USA.
pages cm
Includes bibliographical references and index.
ISBN 978-0-415-62154-0 (hardback) — ISBN 978-0-203-50341-6 (eBook PDF)
1. Approximation algorithms. 2. Functional analysis. 3. Probabilities.
4. Markov processes. I. Title.
QA76.9.A43A46 2014
519.2 33—dc23
2013041800
Published by: CRC Press/Balkema
P.O. Box 11320, 2301 EH Leiden,The Netherlands
e-mail:
Pub.NL@taylorandfrancis.com
www.crcpress.com
–
www.taylorandfrancis.com
ISBN: 978-0-415-62154-0 (Hardback)
ISBN: 978-0-203-50341-6 (eBook PDF)
Table of contents
1
Introduction
1
PART I
Mathematical background
2
Real analysis and linear algebra
2.1 Definitions and notation
2.1.1 Numbers, sets and vectors
2.1.2 Logical notation
2.1.3 Set algebra
2.1.4 The supremum and infimum
2.1.5 Rounding off
2.1.6 Functions
2.1.7 Sequences and limits
2.1.8 Infinite series
2.1.9 Geometric series
2.1.10 Classes of real valued functions
2.1.11 Graphs
2.1.12 The binomial coefficient
2.1.13 Stirling’s approximation of the factorial
2.1.14 L’Hôpital’s rule
2.1.15 Taylor’s theorem
2.1.16 The
l
p
norm
2.1.17 Power means
2.2 Equivalence relationships
2.3 Linear algebra
2.3.1 Matrices
2.3.2 Eigenvalues and spectral decomposition
2.3.3 Symmetric, Hermitian and positive definite matrices
2.3.4 Positive matrices
2.3.5 Stochastic matrices
2.3.6 Nonnegative matrices and graph structure
3
5
5
5
6
6
7
7
7
8
9
11
11
12
13
13
14
14
14
15
16
16
16
18
21
22
24
25

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin