|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Baker G.A., Graves-Morris P. — Pade approximants (vol. 1) |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
 -Algorithm I:80—84
 -Algorithm I:76—80 84—90
-Algorithm, for vector sequences II:55
-Algorithm, generalized II: 14— 16
 . Pade approximants of I:43 47 142—147 154 II:19
 . Pade approximants of I:43—47 141—147 156
 . Pade approximants of I:43 47 141—147 154—155
A-stability II:151
Acceleration of convergence I:16—17 69—90
Accuracy, numerical I:58—65
Accuracy-through-order I:1—2
Aitken's  method I:69—74
Algorithms for rational interpolation II:6—17
Anharmonic oscillator II:170—171
Arzela's theorem I:175
Associated continued fraction 1.127
Asymptotic convergence I:200
Asymptotic expansion I:221
Backward recurrence method I:115
Baker algorithm I:66
Baker definition I:21—22; II:52
Baker — Gammel approximants II:21 —32 63
Baker — Gammel approximants, asymptotic II:30—31
Baker, Gammel and Wills, conjecture of I:286
Baker, Gammel and Wills, theorem of I:32—33
Beardon's theorems I:237
Behte — Salpeter equation II: 108—113
Bigradients I:37—42 136—137
Bigradients, polynomial I:39
Binomial function I:139 144
Biorthogonal algorithm II:76—79
BLOCKS I:24—31
C(L/M), definition of I:21
C-fraction I:127
C-table I:22—23 29 31
Calculation of Pade approximants, algebraic I:8—14 43—48 66—68
Calculation of Pade approximants, numerical I:61—68
Canterbury approximants II:41—45
Capacity I:274—284
Cardioid theorem I:151
Carleman's criterion, application of II:169
Carleman's criterion, for Hamburger series I:223
Carleman's criterion, for Stieltjes series I:200—202
Cartan's Lemma I:274
Cauchy — Binet formula I:239—240
Cauchy — Jacobi problem II: 1
Characteristic function II:128—132
Chebychev see Tchebyscheff
Chisholm approximants II:41—43
Chordal metric I:256—263
Clenshaw-Lord algorithm II:58—60
Coefficient problem I:65; II:7
Collocation II:138—145
Complementary error function I:140 144
Continued fractions I:103—157
Continued fractions, associated I:127
Continued fractions, contraction of I:127 147
Continued fractions, convergents of see convergents
Continued fractions, corresponding I:127
Continued fractions, definition I:104—105 107
Continued fractions, divergence condition for I:148
Continued fractions, elements of I:104 119
Continued fractions, equivalence transformation of I:105—107
Continued fractions, periodic I:117 138
Continued fractions, recurrence relations for I:106 109 135
Continued fractions, regular corresponding I:127
Continued fractions, repeating I:117—138
Continued fractions, summation formula I:115—116
Continued fractions, terminating I:104
Convergence, in capacity I:274—284
Convergence, in measure I:263—274
Convergence, of row sequences I:238 261
Convergents I:104 111—112 117—119
Cordellier's identity I:88
Crank — Nicholson methods II: 145—153
Critical point methods I:55—57 59—61 II:32—40 178
D(m, n), definition of I:162
D-log Pade approximants I:55; II:33
Dawson integral I:141
Dawson integral, generalized II:19
de Montessus's theorem I:241—252
de Montessus's theorem, generalization of I:254; II:161
Defect I:53—55 58—59
Deficiency index I:20
Density function, construction of I:180—181
Determinancy of moment problem I:17 179 193 197—207
Determinantal formulas for Pade approximants I:4—8. 43—48
Determinantal identities for Stieltjes series coefficients I:165—166
Determinantal inequalities I:227 235
Determinantal inequalities, for Hamburger series coefficients I:227 235
Determinantal inequalities, for Stieltjes series coefficients I:208 209
Diagonal sequences I:236
Diffusion processes II: 145—153
Divergence condition I:148 156—157
Divided differences II:2
Duality I:31 236
Equicontinuity I:174—176
Equicontinuous sequences I:210 261
Equivalence transformation I:105—106
Error formula for Pade approximants of Hamburger series II:128—129
Error formula for Pade approximants of Stieltjes I:185 189—193;
Error formula for Pade approximation I:6 250
Error formula from variational principles II:103—106
Error function I:141 II:19—20
Essential singularity I:49
Euclidean algorithm I:66 134—135
Euler — Maclaurin sum formula II:130
Euler's corresponding fraction I:137—139
Euler's function and series I:17—18 200—202
Euler's recurrence theorem I:106
Euler's summation formula I:115—116
Existence of Pade approximants I:27
Exploding vacuum II:166—167
Exponential approximants II:28
Exponential function, continued fractions for I:139—143
Exponential function, Pade approximants for I:8—14
Exponential function, Saff — Varga theorems for I:229—233
Exponential integral, continued fraction for I:140; 144 II:164—165
Exponential integral, first order I:186
Extended Stieltjes series see Hamburger series
Factorization II:43
Fisher approximants II:45
Forward recurrence method I:114—115
Frobenius definition I:20 22
Frobenius identities I:85 90—93
Gamma function, Binet's formula for I:202—205
Gammel — Guttman — Gaunt — Joyce approximants II:33—36
Gammel's counterexample I:285
Gaussian quadrature II:127—132
General C-fraction I:129
Gnomic theory II:74
Green's functions, bound-state II:113
Green's functions, partial wave, free II:89
Green's functions, partial wave, Jost solution II:90
Green's functions, partial wave, momentum space II:114
Green's functions, partial wave, standing wave, free II:89
Green's functions, S-wave, exponential potential II:98
Green's functions, three-dimensional, free II:81
Green's functions, three-dimensional, relativistic, free II: 108
Green's functions, three-dimensional, relativistic, standing wave, free II:109
Green's functions, three-dimensional, standing wave, free II:85
Gregory's series I:78 81
Hadamard's determinant theorem I:39—42 243
Hamburger functions as real J-fractions I:225
Hamburger moment, definition of I:208 222
Hamburger series, definition of I:208 222
Hamburger's theorem I:221
Hankel determinant I:7 41
Hankel matrix, condition number of I:64—65
Hardy's puzzle I:78—80
| Hausdorff measure, a-dimensional I:283
Hausdorff moment problem I:193—196
Herglotz functions I:225—227
Hermite's formula I:250; II:2
High field expansions II:179
Hilbert space methods II:46 68—72 103—107
Homographic invariance I:32—33 II:42—43 45 53
Hughes Jones approximants II:43—45
Hyperbolic tangent I:139 143—144
Hypergeometric functions I:141—147 197—198
Identities for neighboring approximants I:90—96
Inclusion regions I:171 206
Incomplete gamma function I:140 141 145 II:19
Inequalities, for density function II:132—138
Inequalities, for moments I:186
Integer moment problem I:196—197
Integral equations II:64—79
Interlacing I:168—169 210 227;
Invariance, homographic I:32—33; II:42—43 45 53
Inverse hyperbolic tangent I:140 144
Inverse tangent I:139 144;
J-fraction I:128
Jost method II:121—122
K-matrix II:85 107 110—112
Kernels, compact II:67—72
Kernels, completely continuous II:67—72
Kernels, finite rank II:65—67 72
Kronecker's algorithm I:66; II:7
L-stability II:151
Laguerre polynomials I:186
Laguerre's method II: 165
Lanczos  -method II:138—145
Lanczos biorthogonal method II:76
Laplace transform, inversion of II: 153—155
Lattice-cutoff field theory II:176—178
Laurent's theorem I:49
Le Roy function II:32
Lemniscates I:274—284
Lippman — Schwinger equation II:82—83 113
Logarithmic capacity I:283
Markov problem II:137
Matrix Pade approximants II:50—56
Measure, convergence in I:263
Meromorphic functions, convergence of sequences of I:259
Mittag — Leffler star I:50
Moment bounds I:186
Moment method II:46
Moment problems I:178— 179
Moment, definition of Hamburger I:208 222
Moment, definition of Hausdorff I:195
Moment, definition of Stieltjes I:158
Moments, bounds for I:186; II:132—138
Multi-index I:239
Multipoint Pade approximation I:254; II:1—31
Multipole I:49
Multivariable approximants II:40—50
N-point Pade approximants II:1—31
Natural logarithm I:140 144
Newton interpolating polynomials II:2—3
Newton — Pade approximants II:1—31
Nuttall's compact form I:16
Nuttall's theorem I:269
Orthogonal polynomials I:82—86 209—210 255—256
Osculatory rational interpolation II:1—31
P-fraction I:130—131
Pade approximant I:1—288; II:1—180
Pade denominator, definition of I:4
Pade equations I:2—3
Pade numerator, definition of I:6
Pade table I:7—8 27—31
Pade — Borel approximation II:29—30
Pade — Fourier approximants II:62—63
Pade — Frobenius definition I:20 22
Pade — Legendre series II:21—29
Pade — Tchebycheff approximants II:56—62
Parabola theorem for continued fractions I:150
Parabola theorem of Saff and Varga I:229—232
Paradiagonal sequences I:236
Peres model II:167
Perron's counterexample I:238
Pion-Pion scattering II: 172—176
Poles and zeros for Hamburger functions I:209 227
Poles and zeros for Stieltjes functions I:186 193
Poles and zeros of Pade approximants I:31 49—59 96—102 126 166 263
Poloids II:175
Polya frequency series I:227—235
Pommerenke's theorem I:271
Potential scattering II:79—126
Projection techniques II:72—79
Prong method II:43—44
Prym's function I:140 147
Q. D. algorithm I:99 125—126
Q. D. algorithm, for T-fractions II:20
Q. D. algorithm, generalized II:13—14
Q. D. Table I:99 125—126
Quadratic approximants II:36—37 49
Quadrature II:127—132
Quantum theory, connection with II:79—126
Quasi-analytic functions I:51
Ratio method II:33
Rational approximation II:155—162
Rational interpolation II:1—31
Ray sequences I:191
Real J-fractions I:128 225
Real symmetric functions I:160—161 180
Regular C-fraction I:127
Reliability I:63 132:
Rhombus rule I:77 81
Riccati equation, Pade approximants for II:162—165
Riemann sphere I:257
Root problem I:96—102
Rouche's theorem I:279
Runge's theorem II:158—159
S-fraction I:127—128 165 206
S-fraction for I:165
S-matrix, partial wave II:89 91
Saff s theorem I:254
Scattering theory, quantum mechanical II:80—92
Schwarz's lemma I:189 192
Sectorial theorem of Saff and Varga I:229
Seidel's theorem I:148—150
Sequence, acceleration of convergence of I:16—17 69—90
Sequence, column I:30
Sequence, diagonal I:17 32 35
Sequence, paradiagonal I:30
Sequence, row I:30
Series analysis I:55—57 59—61;
Series, acceleration of convergence of I:16—17 69—90
Shafer approximants II:36—37
Single-sign potentials II:106—114
Singular potentials II:120—126
Spherical convergence I:256—263
Star Identity I:23
Stieltjes function I:158 208
Stieltjes function, definition of I:158 221
Stieltjes function, numerical calculation of I:64
Stieltjes inversion formula I:221
Stieltjes series I:158 208
Stieltjes series, definition of I:158 221
Stieltjes series, example of I:161
Stieltjes series, inequalities for Pade approximants of I:170
Sturm sequence I:167
Sylvester's theorem I:23 167
T-fractions I:138; II:17—21
T-matrix II:81—82 103 172—176
T-matrix, partial wave II:89
T-matrix, Toeplitz matrix I:67
T-matrix, Totally monotone sequence I:195
T-matrix, Totally positive series I:228
T-matrix, Trudi's theorem I:42
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå