Handbook of numerical analysis applications: with programs for engineers and scientists
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
McGraw-Hill
1984
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Getr. Zählung zahlr. graph. Darst. |
| ISBN: | 0070480575 |
Internformat
MARC
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| 100 | 1 | |a Pachner, Jaroslav |d 1955- |e Verfasser |0 (DE-588)132555441 |4 aut | |
| 245 | 1 | 0 | |a Handbook of numerical analysis applications |b with programs for engineers and scientists |c Jaroslav Pachner |
| 264 | 1 | |a New York, NY [u.a.] |b McGraw-Hill |c 1984 | |
| 300 | |a Getr. Zählung |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Analyse numérique - Informatique | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 4 | |a Numerical analysis |x Data processing | |
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Datensatz im Suchindex
| _version_ | 1804116559451389952 |
|---|---|
| adam_text | Contents
Preface xv
PART ONE THEORY
1. Linear Algebra I 1.1
1.1 Systems of Linear Algebraic Equations 1.1
1.2 Matrices 1.2
1.3 Determinants and the Inverse Matrix 1.5
1.4 Direct Methods 1.8
1.5 Error Analysis 1.13
1.6 Overdetermined System of Equations 1.20
1.7 Iterative Methods 1.21
2. Interpolation, Approximation, and Numerical Differentiation 2.1
2.1 Interpolation Techniques 2.1
2.2 Lagrange Interpolation 2.3
2.3 Newton Interpolation 2.5
2.4 Hermite Interpolation 2.8
2.5 Cubic Spline Interpolation 2.10
2.6 Trigonometric Interpolation 2.14
2.7 Inverse Interpolation 2.15
2.8 Least Squares Techniques 2.15
2.9 Approximation by Chebyshev Polynomials 2.17
2.10 Approximation by Orthogonal Polynomials with Arbitrarily Distrib¬
uted Abscissas 2.19
2.11 Approximation of a Periodic Function 2.21
vii
viii contents
2.12 Economization of a Power Series 2.23
2.13 Approximation by a Rational Function 2.24
2.14 Numerical Differentiation 2.27
2.15 Choosing the Method 2.30
3. Evaluation of Definite Integrals 3.1
3.1 Methods of Numerical Integration 3.1
3.2 Integrals with Numerically Defined Integrands 3.4
3.3 Integrals over Finite Intervals 3.5
3.4 Integrals over Semi Infinite Intervals 3.6
3.5 Integrals over Infinite Intervals 3.7
3.6 Romberg Integration 3.8
3.7 Singular Integrals 3.10
4. Ordinary Differential Equations 4.1
4.1 Definitions and Analytical Methods of Integration 4.1
4.2 Differential Equations Defining Special Functions 4.12
4.3 Euler and Taylor Series Methods 4.16
4.4 Runge Kutta Methods 4.20
4.5 Predictor Corrector Methods 4.24
4.6 Stability and Accuracy of Integration Methods 4.31
4.7 Choosing the Method 4.32
5. Boundary Value Problems of Ordinary Differential Equations 5.1
5.1 Analytical Approach to Boundary Value Problems 5.1
5.2 Orthogonal Eigenfunctions Defined as Solutions of a Boundary
Value Problem 5.6
5.3 Numerical Approach to Boundary Value Problems 5.11
6. Nonlinear Equations 6.1
6.1 Direct Methods for Algebraic Equations 6.1
6.2 Iterative Methods 6.5
6.3 Real Roots of Algebraic and Transcendental Equations 6.9
6.4 Complex Roots of Algebraic Equations 6.11
6.5 Analysis of Errors in Roots of Algebraic Equations 6.12
6.6 Real Roots of a System of Nonlinear Equations 6.13
7. Linear Algebra II 7.1 !
7.1 Algebraic Eigenvalue Problem 7.1 !
7.2 Numerical Computation of the Eigenvalues of a Real Matrix 7.3
7.3 Eigenvectors 7.5
8. Special Functions 8.1
8.1 The Polynomial Function 8.1
8.2 Orthogonal Polynomials 8.2
8.3 Hypergeometric Series and Confluent Hypergeometric Functions 8.3
8.4 Incomplete Elliptic Integrals of the First, Second, and Third Kind 8.5
CONTENTS IX
8.5 The Bessel Function JJx) and Modified Bessel Function IJx) of
Integer Order 8.6
8.6 The Bessel Function Jv(x) of Order v % 8.6
8.7 The Bessel Function Yv(x) of Order v 8.7
8.8 The Modified Bessel Function K^x) 8.7
8.9 The Spherical Bessel Functions jJx) and yjx) 8.7
8.10 The Gamma Function of a Real Argument 8.8
8.11 The Gamma Function F(| + n) for n = 0, ± 1, ± 2,... 8.9
8.12 The Incomplete Gamma Function 8.9
8.13 The Beta Function 8.9
8.14 The Error Function 8.10
8.15 The Fresnel Integrals C{x) and S(x) 8.11
8.16 The Sine Integral and Cosine Integral 8.11
8.17 The Exponential Integral and Logarithmic Integral 8.12
8.18 The Gudermannian and Its Inverse 8.13
9. Selected Problems of Mathematical Statistics 9.1
9.1 Elements of Combinatorial Analysis 9.1
9.2 Basic Concepts of Mathematical Statistics 9.2
9.3 Curve Fitting 9.5
9.4 Binomial and Negative Binomial Distribution 9.9
9.5 Hypergeometric Distribution 9.10
9.6 Poisson Distribution 9.11
9.7 Normal Distribution and Inverse Normal Distribution 9.11
9.8 Chi Square Distribution 9.13
9.9 t Distribution 9.14
9.10 F Distribution 9.14
References R.I
PART TWO PROGRAMS IN BASIC P.I
Using the Programs P.3
1. Linear Algebra I P.7
PI01 Condition Indicator for a System of Linear Algebraic Equations P.7
PI02 Solution of a System of Linear Algebraic Equations by the Doolit
tle Method with Partial Pivoting and/or Computation of the Deter¬
minant P l 1
PI03 Solution of a Tridiagonal System of Linear Algebraic Equations P. 17
P104 Solution of a Pentadiagonal System of Linear Algebraic Equations P.21
PI05 Reduction of an Overdetermined System of Linear Algebraic Equa¬
tions to a Determined System of Normal Equations P.25
PI06 Iterative Methods for a System of Linear Algebraic Equations:
Jacobi, Gauss Seidel, and Successive Overrelaxation Methods P.27
2. Interpolation, Approximation, and Numerical Differentiation P.31
P201 Lagrange Interpolation P.31
X CONTENTS
P202 Lagrange Interpolation with Equally Spaced Abscissas P.34 ,
P203 Newton Interpolation for the Function and Its First and Second
Derivatives P. 37
P204 Newton Interpolation with Equally Spaced Abscissas for the Func P.41
tion and Its First and Second Derivatives
P205 Hermite Interpolation for the Function and Its First and Second P.44
Derivatives
P206 Hermite Interpolation with Equally Spaced Abscissas for the Func P.48
tion and Its First and Second Derivatives
P207 Hermite Interpolation of a Function Defined at Two Points by the
Function and Its First and Second Derivatives for the Function
and Its First and Second Derivatives P. 52
P208 Cubic Spline for the Function and Its First and Second Derivatives P.55
P209 Cubic Spline with Equally Spaced Abscissas for the Function and
Its First and Second Derivatives P.60
P210 Trigonometric Interpolation P 65
P211 Least Squares Approximation by Chebyshev Polynomials for the
Function and Its First and Second Derivatives P.68
P212 Least Squares Approximation by Orthogonal Polynomials with Ar¬
bitrarily Spaced Abscissas and a Given Weight Function for the
Function and Its First and Second Derivatives P.73
P213 Least Squares Approximation by Orthogonal Polynomials with Ar¬
bitrarily Spaced Abscissas and a Weight Function Equal to 1 for the
Function and Its First and Second Derivatives P.79
P214 Least Squares Approximation by Orthogonal Polynomials with
Equally Spaced Abscissas and a Given Weight Function for the
Function and Its First and Second Derivatives P. 84
P215 Least Squares Approximation by Orthogonal Polynomials with
Equally Spaced Abscissas and a Weight Function Equal to 1 for the
Function and Its First and Second Derivatives P.90
P216 Least Squares Approximation of a Periodic Function (Fourier
Series) for the Function and Its First and Second Derivatives P.95
P217 Least Squares Approximation of an Even Periodic Function (Fou¬
rier Series) for the Function and Its First and Second Derivatives P. 100 .
P218 Least Squares Approximation of an Odd Periodic Function (Fou¬
rier Series) for the Function and Its First and Second Derivatives P. 104
P219 Economization of a Power Series P. 108
P220 Pade Approximation of a Truncated Series with 8 Terms for the
Function and Its First and Second Derivatives P.I 11
P221 Modified Pade Approximation of a Truncated Series with 13 Terms
for the Function and Its First and Second Derivatives P.I 14 |
P222 Least Squares Approximation by a Rational Function with
Chebyshev Polynomials for the Function and Its First and Second
Derivatives P.I 18
P223 Numerical Differentiation: First and Second Derivatives of a Func¬
tion Defined by 3, 5, or 7 Points with Equally Spaced Abscissas P. 124
3. Evaluation of Definite Integrals P.128 ;
P301 Integration of a Numerically Defined Integrand by Composite
Simpson s Rule P.128
CONTENTS xi
P302 Integration of a Numerically Defined Integrand by Modified Com¬
posite Simpson s Rule P. 130
P3O3 Integration of a Numerically Defined Integrand with Equally
Spaced Abscissas by Composite Corrected Trapezoidal Rule P. 132
P304 Integration of a Numerically Defined Integrand with Arbitrarily
Spaced Abscissas by Composite Corrected Trapezoidal Rule P. 134
P305 Composite Gaussian Integration of an Integral over a Finite Inter¬
val P. 136
P306 Laguerre Integration of an Integral over a Semi Infinite Interval P.138
P307 Composite Gauss Laguerre Integration of an Integral over a Semi
Infinite Interval P.140
P308 Hermite Integration of an Integral over an Infinite Interval P.143
P309 Composite Gauss Laguerre Integration of an Integral over an Infi¬
nite Interval P. 144
P310 Romberg Integration P. 147
P311 Chebyshev Gauss Integration of a Singular Integral P. 149
P312 Integration of an Integral with Logarithmic Singularity P. 150
4. Ordinary Differential Equations P.151
P401 Fourth Order Taylor Series Method for a Set of Differential Equa¬
tions of First Order P.151
P402 Fourth Order Taylor Series Method for a Set of Differential Equa¬
tions of Second Order P. 156
P403 Fourth Order Standard Runge Kutta Method for a Set of Differ¬
ential Equations of First Order P. 160
P404 Gill s Version of Fourth Order Runge Kutta Method for a Set of
Differential Equations of First Order P. 164
P405 Third Order Predictor Corrector Method for a Set of Differential
Equations of First Order P.168
P406 Fourth Order Predictor Corrector Method for a Set of Differential
Equations of First Order P. 173
P407 Fourth Order Predictor Corrector Method for a Set of Differential
Equations of Second Order P. 178
5. Boundary Value Problems of Ordinary Differential Equations P.183
P501 Lagrange Interpolation for Boundary Value Problems of One Or¬
dinary Differential Equation of Second Order P.183
6. Nonlinear Equations P.186
P601 Roots of a Quadratic Equation P.186
P602 Roots of a Cubic Equation P. 188
P603 Roots of a Biquadratic Equation P. 190
P604 Preliminary Location of Real Roots of a Nonlinear Equation P. 193
P605 Real Roots of a Nonlinear Equation (with Deflation Subroutine for
an Algebraic Equation) P. 196
P606 Real and Complex Roots of an Algebraic Equation (with Deflation
Subroutine) P.201
Xii CONTENTS
P607 Real Roots of Two Nonlinear Equations by Fixed Point Iteration P.209
P608 Real Roots of Two Nonlinear Equations by the Newton or Modi¬
fied Newton Method P 211
7. Linear Algebra II P.213
P701 Preliminary Location of Eigenvalues by the Gershgorin Method P.213
P702 Coefficients of a Secular Equation by the Krylov Method P.216
P703 Real and Complex Eigenvalues of a Real Matrix from a Secular
Equation P 221
P704 Orthonormal Eigenvectors of a Real Matrix with Simple Real Ei¬
genvalues P.229
8. Special Functions P.235
P801 The Polynomial Function and Its First and Second Derivatives P.235
P802 Orthogonal Polynomials of Legendre, Laguerre, Hermite, and
Chebyshev of the First and Second Kind, Their First and Second
Derivatives, and Zeros of Chebyshev Polynomials of the First Kind P.238
P803 The Hypergeometric Series, Confluent Hypergeometric Function,
Their First and Second Derivatives, the Exponential Integral and
Logarithmic Integral P.242
P804 Incomplete Elliptic Integrals of the First, Second, and Third Kind,
Bessel Functions Jn(x) and Modified Bessel Functions IJx) of In¬
teger Order, the Incomplete Gamma Function, the Error Function,
Fresnel Integrals C(x), S(x), and Sine and Cosine Integrals in Single
Precision P.246
P805 Incomplete Elliptic Integrals of the First, Second, and Third Kind,
Bessel Functions Jn(x) and Modified Bessel Functions In(x) of In¬
teger Order, the Incomplete Gamma Function, the Error Function,
Fresnel Integrals C(x), S(x), and Sine and Cosine Integrals in
Double Precision P.250
P806 Bessel Functions Jv(x), Yv(x), Kv(x) (v Is Any Real Number j),
and Spherical Bessel Functions jn(x), yn(x) (n Is Zero or Any Posi¬
tive Integer) in Single Precision P.256
P807 Bessel Functions Jv(x), Yv(x), Kv(x) (v Is Any Real Number $),
and Spherical Bessel Functions jn(x), yjx) (n Is Zero or Any Posi¬
tive Integer) in Double Precision P.260
P808 Spherical Bessel Functions jjx), yn{x) of Order n = 0,..., 9 P 267
P8O9 Gamma Function of a Real Argument P.270
P810 Gamma Function of Argument n + j, n an Arbitrary Integer P.272
P811 Beta Function P 273
P812 Gudermannian, Its Inverse, and Hyperbolic Functions in Single
Precision P 275
9. Selected Problems of Mathematical Statistics P 277
P901 Permutations, Variations, and Combinations P.277
P902 Arithmetic, Geometric, and Harmonic Mean Values, Variances S2,
s2, Standard Deviations S, s, Standard Errors E, e for a Sample of n
Data P.280
P903 Arithmetic Mean Value, Variances S2, s2, Standard Deviations S, s,
Standard Errors E, e for a Sample of Grouped Data P.282
i
contents xiii
P904 Linear, Power, Exponential, and Logarithmic Curve Fit P.284
P905 Binomial Power Curve Fit P.287
P906 Parabolic Curve Fit P.289
P907 Binomial and Cumulative Binomial Distribution P.291
P9O8 Negative Binomial and Cumulative Negative Binomial Distribution P.293
P909 Hypergeometric and Cumulative Hypergeometric Distribution P.295
P910 Poisson and Cumulative Poisson Distribution P.297
P911 Normal Distribution, Chi Square Distribution, t Distribution, F
Distribution P.298
P912 Inverse Normal Distribution P.303
Appendix P.304
PA1 Derived Elementary Functions in Single Precision P.304
PA2 Elementary Functions in Double Precision P.306
PA3 Subroutines for Programming in Double Precision P.311
Index follows Appendix I.I
|
| any_adam_object | 1 |
| author | Pachner, Jaroslav 1955- |
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| classification_tum | DAT 357f MAT 650f |
| ctrlnum | (OCoLC)9019084 (DE-599)BVBBV002105821 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV002105821 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:26Z |
| institution | BVB |
| isbn | 0070480575 |
| language | English |
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| physical | Getr. Zählung zahlr. graph. Darst. |
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| publisher | McGraw-Hill |
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| spelling | Pachner, Jaroslav 1955- Verfasser (DE-588)132555441 aut Handbook of numerical analysis applications with programs for engineers and scientists Jaroslav Pachner New York, NY [u.a.] McGraw-Hill 1984 Getr. Zählung zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse numérique Analyse numérique - Informatique Datenverarbeitung Numerical analysis Numerical analysis Data processing BASIC (DE-588)4004624-2 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 BASIC (DE-588)4004624-2 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001380722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pachner, Jaroslav 1955- Handbook of numerical analysis applications with programs for engineers and scientists Analyse numérique Analyse numérique - Informatique Datenverarbeitung Numerical analysis Numerical analysis Data processing BASIC (DE-588)4004624-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4004624-2 (DE-588)4042805-9 |
| title | Handbook of numerical analysis applications with programs for engineers and scientists |
| title_auth | Handbook of numerical analysis applications with programs for engineers and scientists |
| title_exact_search | Handbook of numerical analysis applications with programs for engineers and scientists |
| title_full | Handbook of numerical analysis applications with programs for engineers and scientists Jaroslav Pachner |
| title_fullStr | Handbook of numerical analysis applications with programs for engineers and scientists Jaroslav Pachner |
| title_full_unstemmed | Handbook of numerical analysis applications with programs for engineers and scientists Jaroslav Pachner |
| title_short | Handbook of numerical analysis applications |
| title_sort | handbook of numerical analysis applications with programs for engineers and scientists |
| title_sub | with programs for engineers and scientists |
| topic | Analyse numérique Analyse numérique - Informatique Datenverarbeitung Numerical analysis Numerical analysis Data processing BASIC (DE-588)4004624-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analyse numérique Analyse numérique - Informatique Datenverarbeitung Numerical analysis Numerical analysis Data processing BASIC Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001380722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pachnerjaroslav handbookofnumericalanalysisapplicationswithprogramsforengineersandscientists |