The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order (Volume 111) (Mathematics in Science and Engineering, Volume 111) - Hardcover
Synopsis
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.
- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
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About the Author
Keith B. Oldham is Professor of Chemistry at Trent University in Ontario, and Jerome Spanier is a research mathematician at the University of California at Irvine.
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Fractional Calculus (Mathematics in Science and Engineering, Vol. 111) (Volume 111)
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Fractional Calculus (Mathematics in Science and Engineering, Vol. 111) (Volume 111)
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Fractional Calculus (Mathematics in Science and Engineering, Vol. 111) (Volume 111)
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The fractional calculus theory and applications of differentiation and integration to arbitrary order Keith B. Oldham, Jerome Spanier. Mathematics in science and engineering 111.
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Orlando Fla., Academic press, 1974
ISBN 10: 0125255500
ISBN 13: 9780125255509
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Hardcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 26 OLD 9780125255509 Sprache: Englisch Gewicht in Gramm: 550. Seller Inventory # 2499740
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The Fractional Calculus
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Academic Press, 1974
ISBN 10: 0125255500
ISBN 13: 9780125255509
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The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order (Volume 111) (Mathematics in Science and Engineering, Volume 111).
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Gebundene Ausgabe, Gr.-8°. Condition: Gut. 322 S. Das Buch ist in gutem, sauberen Zustand. Einband minimal berieben / fleckig. Ecken und Kanten leicht bestossen. Sonst sauberes und wohlerhaltenes Exemplar. -----Inhalt:. Studies theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. This title considers many computing techniques, such as methods of operator approximation with any given accuracy; methods of covariance matrix estimation; and, methods for low-rank matrix approximations.In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. 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 and Reconstruction 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 ISBN: 9780125255509 Wir senden umgehend mit beiliegender MwSt.Rechnung. Sprache: Englisch Gewicht in Gramm: 570. Seller Inventory # 669007
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The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order Mathematics in Science and Engineering Volume 111
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gebundene Ausgabe. Condition: Gut. 234 Seiten; Leichte altersbedingte Anbräunung des Papiers. Schnitt und Einband sind etwas staubschmutzig; Einbandkanten sind leicht bestoßen; der Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. ENGLISCH. Sprache: Englisch Gewicht in Gramm: 560. Seller Inventory # 1720456
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The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Mathematics in Science and Engineering, Volume 111)
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Elsevier Science, Academic Press, 1974
ISBN 10: 0125255500
ISBN 13: 9780125255509
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Hardcover. Condition: Near Fine. 1st Edition. Red cloth boards, with gilt titles to front and spine and no DW. Small name inside, but an otherwise tight, bright and clean copy with no foxing. 234pp. (16x23.5cm). Please contact us for any more information. Seller Inventory # 7195
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Fractional Calculus (Mathematics in Science and Engineering, Vol. 111) (Volume 111)
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Fractional Calculus (Mathematics in Science and Engineering, Vol. 111) (Volume 111)
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