Data-driven modeling & scientific computation: methods for complex systems & big data
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 629 - 633 |
| Beschreibung: | XVII, 638 S. Ill., graph. Darst. |
| ISBN: | 9780199660346 9780199660339 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
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| 003 | DE-604 | ||
| 005 | 20160122 | ||
| 007 | t | ||
| 008 | 131113s2013 ad|| |||| 00||| eng d | ||
| 020 | |a 9780199660346 |c pbk. |9 978-0-19-966034-6 | ||
| 020 | |a 9780199660339 |c hbk. |9 978-0-19-966033-9 | ||
| 035 | |a (OCoLC)867145743 | ||
| 035 | |a (DE-599)BVBBV041413947 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
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| 084 | |a ST 601 |0 (DE-625)143682: |2 rvk | ||
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| 084 | |a MAT 650f |2 stub | ||
| 084 | |a 65-04 |2 msc | ||
| 084 | |a 65-02 |2 msc | ||
| 100 | 1 | |a Kutz, J. Nathan |e Verfasser |0 (DE-588)1045188867 |4 aut | |
| 245 | 1 | 0 | |a Data-driven modeling & scientific computation |b methods for complex systems & big data |c J. Nathan Kutz |
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2013 | |
| 300 | |a XVII, 638 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 629 - 633 | ||
| 650 | 0 | 7 | |a Big Data |0 (DE-588)4802620-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexes System |0 (DE-588)4114261-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
| 689 | 0 | 1 | |a Komplexes System |0 (DE-588)4114261-5 |D s |
| 689 | 0 | 2 | |a Big Data |0 (DE-588)4802620-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026861181&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026861181 | ||
Datensatz im Suchindex
| _version_ | 1804151526882541568 |
|---|---|
| adam_text | Contents
Prolegomenon
xiii
How to Use This Book
xv
About
MATLAB
xviii
PART I Basic Computations and Visualization
MATLAB
Introduction
1.1
Vectors and Matrices
З
1.2
Logic, Loops and Iterations
9
1.3
Iteration: The Newton-Raphson Method
13
1.4
Function Calls. Input/Output Interactions and Debugging
18
1.5
Plotting and Importing/Exporting Data
23
Ql.
Linear Systems
31
2.1
Direct Solution Methods for Ax
—
b
31
2.2
Iterative Solution Methods for Ax
—
b
35
2.3
Gradient (Steepest) Descent for Ax
-
b
39
2.4
Eigenvalues, Eigenvectors and Solvability
44
5.
S
Eigenvalues and Eigenvectors for Face Recognition
49
2.6
Nonlinear Systems
56
Curve Fitting
61
3.1
Least Square Fitting Methods
61
3.2
Polynomial Fits and Splines
65
3.3
Data Fitting with
MATLAB
69
jQ
Ni
Numerical Differentiation and Integration
77
4.1
Numerical Differentiation
77
4.2
Numerical Integration
83
4.3
Implementation of Differentiation and Integration
87
VIH
Basic
Optimization
93
SI
I Jtu oMsli.imed Opt
nni/.il ion
(í
)eiiv,itive
f
ire Methods)
93
г>
2 Um
on s
Ι [,ιιικίΙ
(
)|!І
imi
/,ι!
ion
([)г!
ívj
h
ve
Methods)
99
5.3
I
inc,
n
ΙΊογ,ι.
immilli.;
105
SA Siiii|ilc>
Method
HO
5.
S CľfietK
Ab-oiilliins
113
Я
Visualization
119
6.1
Customizing Hots
.ind
Ваѕк
20
Plotting
119
6.2
More 2 ) .md 7j[) Plotting
125
6.3
Movirs
.нні
Animations
131
PART II Differential and Partial Differential Equations
Initial and Boundary Value Problems of Differential Equations
137
7.1
lniti.il Value Problems:
E u
loi.
Runge
Kutia
and Adams
Methods
137
7.2
Error Analysis
foi
Time Stepping Routines
144
7.3
Advanced Time Stepping Algorithms
149
7.4
Boundary Value Problems: The Shooting Method
153
7.5
Implementation of Shooting and
Convergente
Studies
160
7.6
Boundary Value
Problems:
Direct Solve and Relaxation
164
7.7
Implementing
MATLAB
for Boundary Value Problems
167
7.8
Linear Operators and Computing Spectra
172
^fl Finite Difference Methods
180
8.?
Finite Difference Discretization
180
8.2
Advanced Iterative Solution Methods for
Ax b
186
8.3
Fast
Poisson
Solvers: The Fourier Transform
186
8.4
Comparison of Solution Techniques for Ax b: Rules of Thumb
190
5.
S
Overcoming Computational Difficulties
195
Time and Space Stepping Schemes: Method of Lines
200
9.1
Basic Time Stepping Schemes
200
9.2
Time-Stepping Schemes: Explicit and Implicit Methods
205
9.3
Stability Analysis
209
ix
9.4
Comparison of Time Stepping Schemes
213
9.5
Operator Splitting Techniques
216
9.6
Optimizing Computational Performance: Rules of Thumb
219
Methods
225
|Tj Spectral
10.1
Fast Fourier Transforms and Cosine/Sine Transform
225
10.2
Chebychev Polynomials rind Transform
229
10.3
Spectral Method Implementation
233
10.4
Pseudo-Spectral Techniques with Filtering
235
10.5
Boundary Conditions and the Chebychev Transform
240
10.6
Implementing the Chebychev Transform
244
10.7
Computing Spectra: The Floquet-Fourier-Hill Method
249
Finite Element Methods
256
11.1
Finite Element Basis
256
11.2
Discretizing with Finite Elements and Boundaries
261
11.3
MATLAB
for Partial Differential Equations
266
11.4
MATLAB
Partia!
Differential Equations Toolbox
271
PART III Computational Methods for Data Analysis
Statistical Methods and Their Applications
279
12.1
Basic Probability Concepts
279
12.2
Random Variables and Statistical Concepts
286
12.3
Hypothesis Testing and Statistical Significance
294
■ M Time-Frequency Analysis: Fourier Transforms and Wavelets
301
13.1
Basics of Fourier Series and the Fourier Transform
301
13.2
FFT Application: Radar Detection and Filtering
308
13.3
FFT Application: Radar Detection and Averaging
316
13.4
Time-Frequency Analysis: Windowed Fourier Transforms
322
13.5
Time-Frequency Analysis and Wavelets
328
13.6
Multi
Resolution Analysis and the Wavelet Basis
335
13.7
Spectrograms and the
Gábor
Transform in
MATLAB
340
13.8
MATLAB
Filter Design and Wavelet Toolboxes
346
ВСІ
Image Processing and Analysis
358
14.1
li.isn
(
ι
ик
cpls ,md Analysis ol Images
358
14.2
hill ¡I I lllcl
Klí ,
JOI
ІІИ.І^Г
DrilOISIIIj.1,
364
14.3
Diffusion
.md
I
m,
іде
Puh
ілми;;
369
Ш£Ћ
Linear
Algebra
and Singular Value Decomposition
376
15.1
ľi.
ι
m<
,
ol I he
Чіпані,
и
V,
1
1
u«1 D<4
ι
миром
I
ion (SVÍ.))
376
15.2 Ihr
SVI)
m
Uhj.kIi I
( niilexl 381
15.
3
Intiodui lion to Prim
ιρ,ιΙ
С
nmponent Analysis
(РСЛ)
387
15.
4
Prim ip.il
C ompoiienlv
Duitonali/alton
rind
SVD
391
15.5
ľniu
ιρ,ιΙ
Components
and
Propec
Orthogonal Modes
395
15.6
Robust
РСЛ
403
BTjjfl
Independent Component Analysis
412
)6.
1
lhe
Concept of
Independen!
Components
412
16.2
Image Separation Problem
419
163
Image Separation and
MATLAB
424
Image Recognition: Basics of Machine Learning
431
17.1
Recognizing Dogs and
Caís
431
17.2
The
SVD
and Linear Discrimination Analysis
436
17.3
Implementing Cat/Dog Recognition in
MATLAB
445
Basics of Compressed Sensing
449
18.1
Beyond Least-Square Fitting: The
/
Norm
449
18.2
Signal Reconstruction and Circumventing Nyquist
456
18.3
Data (image) Reconstruction from Sparse Sampling
464
9
Dimensionality Reduction for Partial Differential Equations
472
19.1
Modal Expansion Techniques for PDEs
472
19.2
PDE Dynamics in the Right (Best) Basis
478
19.3
Clobai Normal Forms of Bifurcation Structures in PDEs
482
19.4
The POD Method and Symmetries/lnvariances
492
19.5
POD Using Robust PCA
499
χι
Π
Dynamic Mode Decomposition
506
20.1
Theory
oí
Dynamic Mode Decomposition (DMD)
506
20 2
Dynamics of DMD Versus POD
510
20.3
Applications of DMD
515
Data Assimilation Methods
521
21.1
Theory of Data Assimilation
521
21.2
Data Assimilation, Sampling and
Kalman
Filtering
526
21. 3
Data Assimilation for the
Lorenz
Equation
529
Equation-Free Modeling
537
22.1
Multi-Scale Physics: An Equation-Free Approach
537
22.2
Lifting and Restricting in Equation Free Computing
542
22.3
Equation Free Space-Time Dynamics
547
Complex Dynamical Systems: Combining Dimensionality Reduction,
Compressive
Sensing and Machine Learning
551
23.1
Combining Data Methods for Complex Systems
551
23.2
Implementing a Dynamical Systems Library
556
23.3
Flow Around a Cylinder: A Prototypical Example
564
PART IV Scientific Applications
Applications of Differential Equations and Boundary Value Problems
573
24.1
Neuroscience and the Hodgkin-Huxley Model
573
24.2
Celestial Mechanics and the Three-Body Problem
577
24.3
Atmospheric Motion and the
Lorenz
Equations
581
24.4
Quantum Mechanics
585
24.5
Electromagnetic Waveguides
588
Applications of Partial Differential Equations
590
25.1
The Wave Equation
590
25.2
Mode-Locked Lasers
593
25.3
Bőse-Einstein
Condensates
600
XII
2Г>.4
/VIvrihoM
Diffusion
•inel
Af
mosphriic Dyn.imks
604
25
S
Inlioilut
tion
lo Ke,u
tion
Diffusion Systems
611
14.
в
Ste.idv St.itc
f
low
Ovci
,ιη
Aiifoil
616
Applications of Data Analysis
620
26.1
Λπ.ιΙγ/ιιψ,
Musk
St
oies .nul
the
ínihoi li.iiisfonn
620
26.2
I
m.
ще
f )( noisinj;
t
ht
о и
ці і
f il
t
ci ini;
,ιικ
I Diffusion
622
26.^
Osc
iti,il
киї,
M.
iss
,ιγηΙ
Dimcnsioibility
Кссіік
hon
625
26 4
Mlisk Crine
Identitu
«ilion
626
References
629
Index of
MATLAB
Commands
634
Index
636
|
| any_adam_object | 1 |
| author | Kutz, J. Nathan |
| author_GND | (DE-588)1045188867 |
| author_facet | Kutz, J. Nathan |
| author_role | aut |
| author_sort | Kutz, J. Nathan |
| author_variant | j n k jn jnk |
| building | Verbundindex |
| bvnumber | BV041413947 |
| classification_rvk | SK 500 SK 800 SK 900 SK 950 ST 601 |
| classification_tum | DAT 620f MAT 650f |
| ctrlnum | (OCoLC)867145743 (DE-599)BVBBV041413947 |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV041413947 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:56:14Z |
| institution | BVB |
| isbn | 9780199660346 9780199660339 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026861181 |
| oclc_num | 867145743 |
| open_access_boolean | |
| owner | DE-188 DE-83 DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-11 DE-20 DE-29T DE-355 DE-BY-UBR DE-703 |
| owner_facet | DE-188 DE-83 DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-11 DE-20 DE-29T DE-355 DE-BY-UBR DE-703 |
| physical | XVII, 638 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Kutz, J. Nathan Verfasser (DE-588)1045188867 aut Data-driven modeling & scientific computation methods for complex systems & big data J. Nathan Kutz Oxford Oxford Univ. Press 2013 XVII, 638 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 629 - 633 Big Data (DE-588)4802620-7 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s Komplexes System (DE-588)4114261-5 s Big Data (DE-588)4802620-7 s DE-604 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026861181&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kutz, J. Nathan Data-driven modeling & scientific computation methods for complex systems & big data Big Data (DE-588)4802620-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Komplexes System (DE-588)4114261-5 gnd |
| subject_GND | (DE-588)4802620-7 (DE-588)4042805-9 (DE-588)4114261-5 |
| title | Data-driven modeling & scientific computation methods for complex systems & big data |
| title_auth | Data-driven modeling & scientific computation methods for complex systems & big data |
| title_exact_search | Data-driven modeling & scientific computation methods for complex systems & big data |
| title_full | Data-driven modeling & scientific computation methods for complex systems & big data J. Nathan Kutz |
| title_fullStr | Data-driven modeling & scientific computation methods for complex systems & big data J. Nathan Kutz |
| title_full_unstemmed | Data-driven modeling & scientific computation methods for complex systems & big data J. Nathan Kutz |
| title_short | Data-driven modeling & scientific computation |
| title_sort | data driven modeling scientific computation methods for complex systems big data |
| title_sub | methods for complex systems & big data |
| topic | Big Data (DE-588)4802620-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Komplexes System (DE-588)4114261-5 gnd |
| topic_facet | Big Data Numerische Mathematik Komplexes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026861181&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kutzjnathan datadrivenmodelingscientificcomputationmethodsforcomplexsystemsbigdata |