Ãëàâíàÿ    Ex Libris    Êíèãè    Æóðíàëû    Ñòàòüè    Ñåðèè    Êàòàëîã    Wanted    Çàãðóçêà    ÕóäËèò    Ñïðàâêà    Ïîèñê ïî èíäåêñàì    Ïîèñê    Ôîðóì   
blank
Àâòîðèçàöèÿ

       
blank
Ïîèñê ïî óêàçàòåëÿì

blank
blank
blank
Êðàñîòà
blank
Baker G.A., Graves-Morris P. — Pade approximants (vol. 1)
Baker G.A., Graves-Morris P. — Pade approximants (vol. 1)



Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå



Íàøëè îïå÷àòêó?
Âûäåëèòå åå ìûøêîé è íàæìèòå Ctrl+Enter


Íàçâàíèå: Pade approximants (vol. 1)

Àâòîðû: Baker G.A., Graves-Morris P.

Àííîòàöèÿ:

The authors cover applications to statistical mechanics and critical phenomena. There are newly extended sections devoted to circuit design, matrix Pade approximation, computational methods, and integral and algebraic approximants.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/Àíàëèç/Íåïðåðûâíûå äðîáè/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1981

Êîëè÷åñòâî ñòðàíèö: 325

Äîáàâëåíà â êàòàëîã: 05.04.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
blank
Ïðåäìåòíûé óêàçàòåëü
$\eta$-Algorithm      I:80—84
$\varepsilon$-Algorithm      I:76—80 84—90
$\varepsilon$-Algorithm, for vector sequences      II:55
$\varepsilon$-Algorithm, generalized      II: 14— 16
${}_1F_1(\cdot)$. Pade approximants of      I:43 47 142—147 154 II:19
${}_2F_1(\cdot)$. Pade approximants of      I:43—47 141—147 156
${}_2F_n(\cdot)$. 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 $\Delta^2$ 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 $\tau$-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
1 2
blank
Ðåêëàìà
blank
blank
HR
@Mail.ru
       © Ýëåêòðîííàÿ áèáëèîòåêà ïîïå÷èòåëüñêîãî ñîâåòà ìåõìàòà ÌÃÓ, 2004-2024
Ýëåêòðîííàÿ áèáëèîòåêà ìåõìàòà ÌÃÓ | Valid HTML 4.01! | Valid CSS! Î ïðîåêòå