Numerical analysis: an introduction
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2019]
|
| Schriftenreihe: | De Gruyter Graduate
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 175 Seiten Diagramme (teilweise farbig) |
| ISBN: | 9783110573305 |
Internformat
MARC
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| 100 | 1 | |a Heister, Timo |d 1983- |0 (DE-588)1183011571 |4 aut | |
| 245 | 1 | 0 | |a Numerical analysis |b an introduction |c Timo Heister ; Leo G. Rebholz and Fei Xue |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XVII, 175 Seiten |b Diagramme (teilweise farbig) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter Graduate | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
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| 653 | |a Fachhochschul-/Hochschulausbildung | ||
| 653 | |a Finite-Differenzen-Methode | ||
| 653 | |a MATLAB | ||
| 653 | |a Numerische Mathematik | ||
| 689 | 0 | 0 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rebholz, Leo G. |0 (DE-588)1020166274 |4 aut | |
| 700 | 1 | |a Xue, Fei |0 (DE-588)143680803 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-030840759 | ||
Datensatz im Suchindex
| _version_ | 1804179357073145856 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
VII
SOFTWARE
*
IX
ACKNOWLEDGMENT
*
XI
SUPPORT
*
XIII
1
1.1
1.2
1.3
1.3.1
1.3.2
1.4
COMPUTER
REPRESENTATION
OF
NUMBERS
AND
ROUNDOFF
ERROR
*
1
EXAMPLES
OF
THE
EFFECTS
OF
ROUNDOFF
ERROR
*
1
BINARY
NUMBERS
-----
4
64
BIT
FLOATING-POINT
NUMBERS
*
6
ADDING
LARGE
AND
SMALL
NUMBERS
IS
BAD
*
8
SUBTRACTING
TWO
NEARLY
EQUAL
NUMBERS
IS
BAD
*
8
EXERCISES
*
10
2
2.1
2.2
2.3
2.3.1
2.4
2.5
2.6
2.7
2.7.1
2.7.2
2.7.3
2.7.4
2.8
SOLVING
LINEAR
SYSTEMS
OF
EQUATIONS
*
13
SOLVING
TRIANGULAR
LINEAR
SYSTEMS
*
13
FROM
GAUSSIAN
ELIMINATION
TO
LU
FACTORIZATION
*
15
PIVOTING
-----
18
WORKINLU/GE
-----
23
DIRECT
METHODS
FOR
LARGE
SPARSE
LINEAR
SYSTEMS
*
23
CONJUGATE
GRADIENT
*
26
PRECONDITIONING
AND
ILU
-----
28
ACCURACY
IN
SOLVING
LINEAR
SYSTEMS
*
30
MATRIX
AND
VECTOR
NORMS
AND
CONDITION
NUMBER
*
31
CONDITION
NUMBER
OF
A
MATRIX
*
33
SENSITIVITY
IN
LINEAR
SYSTEM
SOLVING
*
34
ERROR
AND
RESIDUAL
IN
LINEAR
SYSTEM
SOLVING
*
36
EXERCISES-----
37
3
3.1
3.2
3.3
3.4
LEAST
SQUARES
PROBLEMS
*
41
SOLVING
LSQ
PROBLEMS
WITH
THE
NORMAL
EQUATIONS
*
42
QR
FACTORIZATION
AND
THE
GRAM-SCHMIDT
PROCESS
*
44
CURVE
OF
BEST
FIT
-----
48
EXERCISES
*
51
4
4.1
FINITE
DIFFERENCE
METHODS
*
53
CONVERGENCE
TERMINOLOGY
*
53
XVI
*
CONTENTS
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.3
4.4
4.5
4.6
APPROXIMATING
THE
FIRST
DERIVATIVE
*
55
FORWARD
AND
BACKWARD
DIFFERENCES
*
55
CENTERED
DIFFERENCE
*
58
THREE
POINT
DIFFERENCE
FORMULAS
*
60
FURTHER
NOTES
-----62
APPROXIMATING
THE
SECOND
DERIVATIVE
*
62
APPLICATION:
INITIAL
VALUE
ODES
USING
THE
FORWARD
EULER
METHOD
*
63
APPLICATION:
BOUNDARY
VALUE
ODES
*
65
EXERCISES
*
69
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
SOLVING
NONLINEAR
EQUATIONS
*
71
CONVERGENCE
CRITERIA
OF
ITERATIVE
METHODS
FOR
NONLINEAR
SYSTEMS
*
71
THE
BISECTION
METHOD
*
72
FIXED-POINT
THEORY
AND
ALGORITHMS
*
77
NEWTON
*
S
METHOD
*
82
SECANT
METHOD
*
86
COMPARING
BISECTION,
NEWTON,
SECANT
METHOD
*
86
COMBINING
SECANT
AND
BISECTION
AND
THE
FZERO
COMMAND
*
87
EQUATION
SOLVING
IN
HIGHER
DIMENSIONS
*
87
EXERCISES
*
90
6
6.1
6.2
6.3
6.4
6.5
EIGENVALUES
AND
EIGENVECTORS
*
93
THEORETICAL
BACKGROUND
*
93
SINGLE-VECTOR
ITERATIONS
*
94
MULTIPLE-VECTOR
ITERATIONS
*
101
FINDING
ALL
EIGENVALUES
AND
EIGENVECTORS
OF
A
MATRIX
*
103
EXERCISES
*
103
7
7.1
7.1.1
7.2
7.3
7.4
7.5
INTERPOLATION
*
105
INTERPOLATION
BY
A
SINGLE
POLYNOMIAL
*
105
LAGRANGE
INTERPOLATION
*
107
CHEBYSHEV
INTERPOLATION
*
110
PIECEWISE
LINEAR
INTERPOLATION
*
113
PIECEWISE
CUBIC
INTERPOLATION
(CUBIC
SPLINE)
*
116
EXERCISES
*
119
8
8.1
8.2
8.3
8.4
8.5
NUMERICAL
INTEGRATION
*
121
PRELIMINARIES
*
121
NEWTON-COTES
RULES
*
124
COMPOSITE
RULES
-----
127
CLENSHAW-CURTIS
QUADRATURE
*
130
GAUSS
QUADRATURE
*
133
CONTENTS
*
XVII
8.6
MATLAB
*
S
INTEGRAL
FUNCTION
-----
138
8.7
EXERCISE-----
139
9
INITIAL
VALUE
PROBLEMS
*
141
9.1
REDUCTION
OF
HIGHER
ORDER
IVPS
TO
FIRST
ORDER
*
142
9.2
THE
FORWARD
EULER
METHOD
-----
143
9.3
HEUN
*
S
METHOD
AND
RK4
-----
146
9.4
STIFF
PROBLEMS
AND
NUMERICAL
STABILITY
*
147
9.4.1
IMPLICIT
METHODS
AND
UNCONDITIONAL
STABILITY
*
149
9.5
SUMMARY,
GENERAL
STRATEGY,
AND
MATLAB
ODE
SOLVERS
-----
150
9.6
FITTING
ODE
PARAMETERS
TO
DATA
*
152
9.7
EXERCISES-----
155
10
PARTIAL
DIFFERENTIAL
EQUATIONS
*
159
10.1
THE
ID
HEAT
EQUATION
*
159
10.1.1
A
MAXIMUM
PRINCIPLE
AND
NUMERICAL
STABILITY
*
166
10.2
THE
2D
POISSON
EQUATION
*
168
10.3
EXERCISES
*
172
INDEX
*
173
|
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| author | Heister, Timo 1983- Rebholz, Leo G. Xue, Fei |
| author_GND | (DE-588)1183011571 (DE-588)1020166274 (DE-588)143680803 |
| author_facet | Heister, Timo 1983- Rebholz, Leo G. Xue, Fei |
| author_role | aut aut aut |
| author_sort | Heister, Timo 1983- |
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| building | Verbundindex |
| bvnumber | BV045455455 |
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| ctrlnum | (OCoLC)1090776086 (DE-599)DNB1168253691 |
| discipline | Mathematik |
| format | Book |
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| publishDateSearch | 2019 |
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| publisher | De Gruyter |
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| series2 | De Gruyter Graduate |
| spelling | Heister, Timo 1983- (DE-588)1183011571 aut Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue Berlin ; Boston De Gruyter [2019] © 2019 XVII, 175 Seiten Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Fachhochschul-/Hochschulausbildung Finite-Differenzen-Methode MATLAB Numerische Mathematik Numerische Mathematik (DE-588)4042805-9 s DE-604 Rebholz, Leo G. (DE-588)1020166274 aut Xue, Fei (DE-588)143680803 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-057332-9 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-057333-6 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030840759&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heister, Timo 1983- Rebholz, Leo G. Xue, Fei Numerical analysis an introduction Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical analysis an introduction |
| title_auth | Numerical analysis an introduction |
| title_exact_search | Numerical analysis an introduction |
| title_full | Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue |
| title_fullStr | Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue |
| title_full_unstemmed | Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue |
| title_short | Numerical analysis |
| title_sort | numerical analysis an introduction |
| title_sub | an introduction |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030840759&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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