Microcomputer algorithms: action from algebra
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bristol u.a.
Hilger
1991
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 235 S. |
| ISBN: | 0750300973 |
Internformat
MARC
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| 100 | 1 | |a Killingbeck, John P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Microcomputer algorithms |b action from algebra |c J. P. Killingbeck |
| 264 | 1 | |a Bristol u.a. |b Hilger |c 1991 | |
| 300 | |a XV, 235 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1804120371593478144 |
|---|---|
| adam_text | Contents
Preface xi
1 General Introduction 1
1.1 The microcomputer style of programming 1
1.2 Modules and subroutines 2
1.3 Notation and conventions of this book 4
1.4 The program presentation format 6
1.5 Brief survey of chapter contents 7
2 Root finding Methods and their Application 9
2.1 General introduction 9
2.2 The root finding approach 9
2.3 Root finding modules 11
2.4 A note on cubic equations 14
2.5 Brief program descriptions and programs 15
ROOTSCAN. NEWTON. SECANT. ZIGZAG. 15
2.6 Extrema and roots 18
2.7 The programs search and maxmin 20
2.8 Expectation values. The integral approach 21
2.9 The energy approach 22
2.10 Calculating local quantities 23
3 The Richardson Extrapolation Method 25
3.1 General introduction 25
3.2 3.9 Microcomputer calculus. An example. Numerical
differentiation. General applications. Richardson versus
Pade The residual error term. The standard
extrapolation formulae. The non standard case. The
general case. The program rich. 25
romberg. Mathematical theory 35
3.10 3.14 Midpoint integration. Finding the A^. A modified
midpoint rule. Relative merits of quadrature rules.
Three point rules. 35
v
vi Contents
romberg. Programming notes 40
3.15 3.17 The subroutine structure. The two point methods.
Three point rules. 40
3.18 rombero. Program analysis and program 41
romberg. Specimen results 44
3.19 3.22 The error integral. End point singularities. Residual
error examples. Final comments. 44
4 Some Interpolation and Extrapolation Methods 50
4.1 General introduction 50
interp. Mathematical theory 50
4.2 4.4 The Lagrange interpolation procedure. The divided
difference approach. Computing derivatives. 50
interp. Programming notes 53
4.5 4.7 Arrays. Variable indices. Derivatives 53
4.8 interp. Program analysis and program 54
interp. Specimen results 55
4.9 4.10 Runge s example. Final comments. 55
spline and spleen. Mathematical theory 57
4.11 4.13 Quadratic splines. The fundamental equations. The
collocation method, spleen. 57
4.14 spline. Program analysis and program 61
spline. Specimen results 62
4.15 Energy level interpolation 62
4.16 spleen. Program analysis and program 63
spleen. Specimen results 65
4.17 Energy level calculations 65
wynn. Mathematical theory 66
4.18 4.22 The Aitken transformation. Multi component sequences.
Pade approximants. Series of Stieltjes. The algorithm. 66
wynn. Programming notes 73
4.23 4.27 Setting array dimensions. Use as a library subroutine.
Labelling the approximants. Storing and displaying the
(M/N). Rounding errors and scaling tests. 73
4.28 wynn. Program analysis and program 76
wynn. Specimen results 78
4.29 4.31 Varying KS. Perturbation series analysis. Comments on
the results. 78
5 The Matrix Inverse and Generalized Inverse 81
5.1 General introduction 81
matin and genfit. Mathematical theory 81
5.2 5.5 Choice of reduction method. Least squares fitting. The
generalized inverse. An example. Parabolic fitting. An
iterative method. 81
Contents vii
matin and genfit. Programming notes 84
5.6 5.7 Program module structure. Forming MTM for genfit. 84
5.8 matin. Program analysis and program 86
5.9 genfit. Program analysis and program 89
genfit. Specimen results 93
5.10 A parallel test 93
5.11 invert. Program analysis and program 95
6 The Matrix Eigenvalue Problem 99
6.1 General introduction 99
jolly. Mathematical theory 99
6.2 6.9 The origin of jolly. Some simple transformations. The
algorithm. The eigencolumns. Eigenvalues by deflation.
Rapid eigenvalue calculation. Non symmetric matrices.
Preliminary transformations. 99
jolly. Programming notes 106
6.10 6.13 The form of R(N, K). The matrix indices. The working
copy, including A. The subroutine structure. 106
6.14 jolly. Program analysis and program 107
jolly. Specimen results 110
6.15 6.17 A 5 x 5 example. Matrices with equal diagonal
elements. Using Aitken extrapolation. 110
folder. Mathematical theory 112
6.18 6.23 Introduction. The perturbation approach. An explicit
example. An alternative approach. Calculating
eigenvectors. Solving linear equations. 112
folder. Programming notes 119
6.24 6.27 Array requirements. The modular structure. Index
permutation. The use of submatrices. 119
6.28 folder. Program analysis and program 120
folder. Specimen results 124
6.29 6.33 Simple test example. A complex matrix example.
Finding double roots. An iterative method. Band
matrices. 124
hitter. Mathematical theory 128
6.34 6.39 The self consistency problem. The Brillouin Wigner
method. The direct iteration procedure. Relaxation
parameters and Rayleigh quotients. The matrix H.
Algebraic matrix elements. 124
hitter. Programming notes 134
6.40 6.42 The relaxation parameter. Displaying the eigencolumn.
The A parameter. 134
6.43 hitter. Program analysis and program 135
hitter. Specimen results 137
6.44 Eigenvalues for betosc 137
6.45 betosc. Program analysis and program 138
6.46 Using folder with betosc 140
viii Contents
7 Two Perturbation Methods 142
7.1 General introduction 142
hyposc. Mathematical theory 142
7.2 7.3 Hypervirial theorems. The perturbation recurrence
relation. 142
hyposc. Programming notes 145
7.4 7.10 Use of the value A = 1. Use of the F factor. Calculation
of array indices. Calculation of (xN). The calculation of
WKB results. Variable a and p. The T array and the
Wynn algorithm. 145
7.11 hyposc. Program analysis and program 147
hyposc. Specimen results 150
7.12 7.13 Perturbed oscillator energies. Recent developments. 150
rally. Mathematical theory 152
7.14 7.15 Convergence criteria. The recurrence relations. 152
rally. Programming notes 154
7.16 7.17 The array problem. Use of A = 1. 154
7.18 rally. Program analysis and program 155
rally. Specimen results 158
7.19 7.21 Rayleigh Schrodinger mode. Brillouin Wigner mode.
Rayleigh iteration mode. 158
8 Finite Difference Eigenvalue Calculations 160
8.1 General introduction 160
radial. Mathematical theory 160
8.2 8.4 The finite difference approximation. The shooting
approach. Expectation values. 160
radial. Programming notes 164
8.5 8.9 Initial conditions. Storage requirements. Node counting.
The choice of L. The index /. 164
8.10 radial. Program analysis and program 166
radial. Specimen results 169
8.11 8.12 The Coulomb potential. A comment on singular
potentials. 169
fidif. Mathematical theory 171
8.13 8.20 The three term recurrence relation. Obtaining h4 error.
Initial and boundary conditions. Forwards and
backwards shooting. The Numerov method. The three
methods of fidif. The propagator approach. Excited
state calculations. 171
fidif. Programming notes 177
8.21 8.24 The range of x. An economical starting procedure. The
boundary conditions. Wavefunction scaling. 177
8.25 fidif. Program analysis and program 180
fidif. Specimen results 183
8.26 8.29 Comparison of methods 2 and 3. Extrapolation for
method 1. Expectation values. Final comments. 183
Contents ix
9 Recurrence Relation Methods 187
9.1 General introduction 187
serat and serosc. Mathematical theory 187
9.2 9.7 The perturbed Coulomb potential. The recurrence
relation. The zero coefficient test. Forwards nested
multiplication. The perturbed oscillator potential. The
false eigenvalue effect. 187
serat and serosc. Programming notes 193
9.8 9.11 Array dimensions. Modular structure. Precomputation.
Reduction in strength. The scaling factor. 193
9.12 serat. Program analysis and program 194
serat and serosc. Specimen results 199
9.13 9.15 Published applications for serat. Some specimen results
for serosc. The CT parameter. 199
momosc. Mathematical theory 201
9.16 9.20 Inner product recurrence relations. The computational
procedure. A link with matrix theory. The angular
momentum variable. A perturbation approach. 201
momosc. Programming notes 205
9.21 The singularity problem 205
9.22 momosc. Program analysis and program 205
momosc. Specimen results 208
9.23 9.24 Comparison with serosc. Some specimen expectation
values. 208
10 Two Research Problems 210
10.1 General introduction 210
twodosc. Mathematical theory 210
10.2 The recurrence relations 210
twodosc. Programming notes 212
10.3 10.4 Array requirements. Exploiting the symmetry. 212
10.5 twodosc. Programming analysis and program 213
twodosc. Specimen results 215
10.6 Results at small A 215
zeeman. Mathematical theory 216
10.7 10.9 Introduction. Implicit basis methods. Using explicit basis
functions. 216
zeeman. Programming notes 220
10.10 10.11 Array requirements. Subroutine structure. 220
10.12 zeeman. Program analysis and program 221
zeeman. Specimen results 224
10.13 Shooting relaxation mode 224
Bibliography 225
Index 231
|
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| language | English |
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| spelling | Killingbeck, John P. Verfasser aut Microcomputer algorithms action from algebra J. P. Killingbeck Bristol u.a. Hilger 1991 XV, 235 S. txt rdacontent n rdamedia nc rdacarrier Algorithmus (DE-588)4001183-5 gnd rswk-swf Mikrocomputer (DE-588)4039206-5 gnd rswk-swf Mikrocomputer (DE-588)4039206-5 s Algorithmus (DE-588)4001183-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003884903&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Killingbeck, John P. Microcomputer algorithms action from algebra Algorithmus (DE-588)4001183-5 gnd Mikrocomputer (DE-588)4039206-5 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4039206-5 |
| title | Microcomputer algorithms action from algebra |
| title_auth | Microcomputer algorithms action from algebra |
| title_exact_search | Microcomputer algorithms action from algebra |
| title_full | Microcomputer algorithms action from algebra J. P. Killingbeck |
| title_fullStr | Microcomputer algorithms action from algebra J. P. Killingbeck |
| title_full_unstemmed | Microcomputer algorithms action from algebra J. P. Killingbeck |
| title_short | Microcomputer algorithms |
| title_sort | microcomputer algorithms action from algebra |
| title_sub | action from algebra |
| topic | Algorithmus (DE-588)4001183-5 gnd Mikrocomputer (DE-588)4039206-5 gnd |
| topic_facet | Algorithmus Mikrocomputer |
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