| Description |
1 online resource (xv, 304 pages) |
| Contents |
Preface -- 1 General introduction and scope of the book -- 1.1 Introduction to post-processing tools -- 1.1.1 Singular value decomposition -- 1.1.2 A toy model to illustrate SVD -- 1.1.3 Proper orthogonal decomposition -- 1.1.4 Higher order SVD -- 1.1.5 A toy model to illustrate HOSVD -- 1.1.6 Applications of SVD and HOSVD -- 1.2 Introduction to reduced order models -- 1.2.1 Data-driven ROMs -- 1.2.2 Projection-based ROMs; 1.3 Organization of the book -- 1.4 Some concluding remarks -- 1.5 Annexes to Chapter 1 -- A. Compact SVD -- B. Truncated SVD -- C. Economy HOSVD -- D. Compact HOSVD -- E. Truncated HOSVD -- 2 Higher order dynamic mode decomposition -- 2.1 Introduction to standard DMD and HODMD -- 2.2 DMD and HODMD: methods and algorithms -- 2.2.1 The standard (optimized) DMD method: the DMD-1 algorithm -- 2.2.2 The DMD-d algorithm with d>1 -- 2.2.3 HODMD for spatially multidimensional data, involving more than one spatial variables -- 2.2.4 Iterative HODMD; 2.2.5 Some key points to successfully use the DMD-d algorithm with d>=1 -- 2.3 Periodic and quasi-periodic phenomena -- 2.3.1 Approximate commensurability -- 2.3.2 Semi-analytic representation of periodic dynamics and invariant periodic orbits in phase space -- 2.3.3 Semi-analytic representation of quasi-periodic dynamics and the associated invariant tori in phase space -- 2.4 Some toy models -- 2.5 Some concluding remarks -- 2.6 Annexes to Chapter 2 -- A. HODMD algorithm: the main program -- B. DMD-d algorithm -- C. DMD-1 algorithm -- D. Reconstruction of the original eld; E. Approximate commensurability -- 3 HODMD applications to the analysis of ight tests and magnetic resonance -- 3.1 Introduction to utter in ight tests -- 3.1.1 Training the method using a toy model for ight tests -- 3.1.2 Using the method in actual ight tests experimental data -- 3.2 Introduction to nuclear magnetic resonance -- 3.2.1 Training the method using a magnetic resonance toy model -- 3.2.2 Using the method with synthetic magnetic resonance experimental data -- 3.3 Some concluding remarks -- 3.4 Annexes to Chapter 3 -- A. Flight test experiments: toy model; B. Nuclear magnetic resonance: toy model -- 4 Spatio-temporal Koopman decomposition -- 4.1 Introduction to the spatio-temporal Koopman decomposition method -- 4.2 Traveling waves and standing waves -- 4.3 The STKD method -- 4.3.1 A scalar state variable in one space dimension -- 4.3.2 Vector state variable with one longitudinal and one transverse coordinate -- 4.3.3 Vector state variable with two transverse and one longitudinal coordinates -- 4.3.4 Vector state variable with one transverse and two longitudinal coordinates -- 4.4 Some key points about the use of the STKD method |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (ScienceDirect, viewed September 22, 2021) |
| Subject |
Decomposition (Mathematics)
|
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Decomposition method.
|
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Decomposition (Mathematics)
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Decomposition method
|
| Form |
Electronic book
|
| Author |
Le Clainche, Soledad, author
|
| LC no. |
2020951376 |
| ISBN |
9780128227664 |
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0128227664 |
|
