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Methods of intermediate problems for eigenvalues: theory and ramifications

Author: Alexander Weinstein; William Stenger
Publisher: New York, Academic Press, 1972.
Series: Mathematics in science and engineering, v. 89.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Studies theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. This book represents a blend of fresh methods in general computational analysis, and  Read more...

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Additional Physical Format: Online version:
Weinstein, Alexander, 1897-
Methods of intermediate problems for eigenvalues: theory and ramifications.
New York, Academic Press, 1972
(OCoLC)643528867
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Alexander Weinstein; William Stenger
ISBN: 0127424504 9780127424507
OCLC Number: 343604
Description: xi, 236 pages 24 cm.
Contents: Preface Contents 1 Overview I Methods of Operator Approximation in System Modelling 2 Nonlinear Operator Approximation with Preassigned Accuracy 2.1 Introduction 2.2 Generic formulation of the problem 2.3 Operator approximation in space C([0; 1]): 2.4 Operator approximation in Banach spaces by polynomial operators 2.5 Approximation on compact sets in topological vector spaces 2.6 Approximation on noncompact sets in Hilbert spaces 2.7 Special results for maps into Banach spaces 2.8 Concluding remarks 3 Interpolation of Nonlinear Operators 65 3.1 Introduction 3.2 Lagrange interpolation in Banach spaces 3.3 Weak interpolation of nonlinear operators 3.4 Some related results 3.5 Concluding remarks 4 Realistic Operators and their Approximation 4.1 Introduction 4.2 Formalization of concepts related to description of real-world objects 4.3 Approximation of R!continuous operators 4.4 Concluding remarks 5 Methods of Best Approximation for Nonlinear Operators 5.1 Introduction 5.2 Best Approximation of nonlinear operators in Banach spaces: Deterministic case 5.3 Estimation of mean and covariance matrix for random vectors 5.4 Best Hadamard-quadratic approximation 5.5 Best polynomial approximation 5.6 Best causal approximation 5.7 Best hybrid approximations 5.8 Concluding remarks II Optimal Estimation of Random Vectors 6 Computational Methods for Optimal Filtering of Stochastic Signals 6.1 Introduction 6.2 Optimal linear Filtering in Finite dimensional vector spaces 6.3 Optimal linear Filtering in Hilbert spaces 6.4 Optimal causal linear Filtering with piecewise constant memory 6.5 Optimal causal polynomial Filtering with arbitrarily variable memory 6.6 Optimal nonlinear Filtering with no memory constraint 6.7 Concluding remarks 7 Computational Methods for Optimal Compression andReconstruction of Random Data 7.1 Introduction 7.2 Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) 7.3 Rank-constrained matrix approximations 7.4 Generic PCA{KLT 7.5 Optimal hybrid transform based on Hadamard-quadratic approximation 7.6 Optimal transform formed by a combination of nonlinear operators 7.7 Optimal generalized hybrid transform 7.8 Concluding remarks Bibliography Index
Series Title: Mathematics in science and engineering, v. 89.
Responsibility: [by] Alexander Weinstein and William Stenger.
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