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BibTeX entry
@Article{Stenger:2000:SSN,
author = "Frank Stenger",
title = "Summary of {Sinc} numerical methods",
journal = j-J-COMPUT-APPL-MATH,
volume = "121",
number = "1--2",
pages = "379--420",
day = "1",
month = sep,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/s0377-0427(00)00348-4;
https://doi.org/10.1137/0712022",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65D15 (65-02)",
MRnumber = "MR1780056 (2001d:65018)",
bibdate = "Sat Feb 25 12:43:36 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
note = "Numerical analysis in the 20th century, Vol.\ I,
Approximation theory",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700003484",
ZMnumber = "0964.65010",
abstract = "This article attempts to summarize the existing
numerical methods based on Sinc approximation. Starting
with a comparison of polynomial and Sinc approximation,
basic formulas for the latter in the one-dimensional
case are given. The author also covers the
following:\par (i) Explicit spaces of analytic
functions for one dimensional Sinc approximation,\par
(ii) applications of Sinc indefinite integration and
collocation to the solution of ordinary differential
equation initial and boundary value problems,\par (iii)
results obtained for solution of partial differential
equations, via Sinc approximation of the
derivatives,\par (iv) some results obtained on the
solutions of integral equations,\par (v) use of Sinc
convolution, a technique for evaluating one and
multi-dimensional convolution-type integrals.\par A
list of some existing computer algorithms based on Sinc
methods is also given.",
abstract2 = "Sinc approximation methods excel for problems whose
solutions may have singularities, or infinite domains,
or boundary layers. This article summarizes results
obtained to date, on Sinc numerical methods of
computation. Sinc methods provide procedures for
function approximation over bounded or unbounded
regions, encompassing interpolation, approximation of
derivatives, approximate definite and indefinite
integration, solving initial value ordinary
differential equation problems, approximation and
inversion of Fourier and Laplace transforms,
approximation of Hilbert transforms, and approximation
of indefinite convolutions, the approximate solution of
partial differential equations, and the approximate
solution of integral equations, methods for
constructing conformal maps, and methods for analytic
continuation. Indeed, Sinc are ubiquitous for
approximating every operation of calculus.",
acknowledgement = ack-nhfb,
classmath = "65D15 (Algorithms for functional approximation) 65-02
(Research monographs (numerical analysis)) 65L60
(Finite numerical methods for ODE) 65M70 (Spectral,
collocation and related methods (IVP of PDE)) 65N35
(Collocation methods (BVP of PDE)) 65R20 (Integral
equations (numerical methods)) 65T40 (Trigonometric
approximation and interpolation)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "algorithms; analytic functions; collocation;
convolution-type integrals; integral equations; Sinc
indefinite integration; Sinc methods; survey article",
reviewer = "H. P. Dikshit (Bhopal)",
}
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114(1)189,
114(2)333,
114(2)387,
115(1)23,
115(1)63,
115(1)397,
116(1)121,
117(2)105,
117(2)159,
119(1)97,
120(1)85,
121(1)ix--x,
121(1)421,
122(1)ix--xi,
122(1)297,
123(1)ix--xii,
123(1)35,
123(1)117,
123(1)261,
124(1)ix--x,
124(1)1,
125(1)xi--xviii,
125(1)57,
125(1)131,
125(1)265,
125(1)297,
125(1)395,
127(1)287,
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128(1)1,
132(1)141,
132(2)255,
133(1)127,
133(1)535,
133(1)601,
133(1)623,
134(1)143,
136(1)123,
137(2)377,
139(2)239,
139(2)323,
140(1)751,
142(1)137,
143(2)291,
144(1)29,
145(1)71,
146(1)11,
146(1)141,
147(1)53,
147(2)349,
147(2)427,
147(2)485,
148(1)213,
149(1)57,
149(1)171,
149(1)279,
149(1)341,
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153(1)61,
154(1)63,
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156(1)23,
156(1)127,
157(1)73,
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159(1)91,
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164(z)107,
164(z)469,
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164(z)797,
166(1)181,
167(1)73,
167(1)183,
168(1)21,
168(1)53,
168(1)65,
168(1)77,
168(1)87,
168(1)155,
168(1)289,
168(1)353,
169(2)377,
171(1)199
- analytic,
116(1)181,
118(1)193,
126(1)277,
126(1)449,
127(1)255,
134(1)85,
137(1)123,
138(2)325,
140(1)713,
145(2)345,
146(2)301,
148(1)29,
148(1)49,
152(1)467,
152(1)493,
160(1)323,
161(2)339,
162(2)467,
164(z)569,
167(1)183,
171(1)235
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113(1)35,
113(1)401,
114(1)81,
114(2)387,
115(1)461,
117(2)121,
118(1)111,
118(1)125,
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120(1)67,
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127(1)173,
128(1)311,
128(1)383,
130(1)163,
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131(1)15,
131(1)149,
133(1)593,
133(1)601,
135(1)1,
136(1)1,
137(1)207,
139(2)275,
141(1)219,
142(1)235,
142(2)389,
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144(1)197,
145(2)417,
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146(1)141,
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151(1)141,
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154(1)175,
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155(2)405,
156(2)433,
157(2)251,
157(2)477,
158(2)407,
159(1)65,
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161(2)339,
163(1)29,
163(1)177,
163(2)433,
163(2)435,
164(z)93,
164(z)207,
164(z)255,
164(z)265,
166(1)153,
168(1)255,
168(1)341,
168(1)353,
168(1)403,
168(1)481,
171(1)311,
172(1)183
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107(2)179,
113(1)141,
113(1)283,
115(1)151,
115(1)229,
115(1)255,
116(1)145,
116(2)263,
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121(1)197,
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146(1)57,
146(2)419,
146(2)443,
146(2)459,
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166(1)247,
166(2)427,
167(2)405,
168(1)447,
169(1)17,
170(1)59,
172(1)65,
172(1)101
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113(1)411,
123(1)117,
127(1)369,
128(1)467,
129(1)209,
130(1)387,
130(1)389,
131(1)507,
132(2)483,
133(1)703,
134(1)369,
135(2)335,
136(1)405,
137(2)399,
138(2)367,
139(2)369,
140(1)877,
140(1)881,
140(1)905,
141(1)283,
142(2)451,
143(2)311,
144(1)375,
145(2)535,
146(2)493,
147(2)517,
148(2)463,
149(2)489,
150(2)397,
150(2)399,
151(2)477,
152(1)613,
153(1)549,
154(2)477,
155(2)461,
156(2)501,
157(2)511,
158(2)507,
159(2)473,
160(1)335,
160(1)337,
161(2)497,
162(2)497,
163(2)465,
164(z)815,
166(2)597,
167(2)499,
168(1)529,
169(2)475,
170(2)467,
170(2)469,
171(1)425,
172(2)409
- based,
107(2)179,
119(1)97,
127(1)1,
130(1)385,
131(1)65,
131(1)361,
132(1)107,
136(1)337,
140(1)231,
140(1)245,
140(1)257,
140(1)499,
140(1)673,
144(1)359,
145(2)319,
150(2)303,
154(1)115,
158(1)43,
162(2)411,
163(1)91,
163(1)139,
163(1)189,
166(1)343,
170(2)317,
172(1)117
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121(1)297,
156(2)355
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118(1)301,
129(1)139,
133(1)567,
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139(2)239,
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147(2)301,
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153(1)73,
153(1)235,
153(1)441,
155(2)423,
156(1)47,
158(1)1,
166(1)221,
169(1)161,
170(2)399
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123(1)1,
123(1)35,
125(1)1
- collocation,
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115(1)309,
119(1)161,
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134(1)243,
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140(1)41,
140(1)381,
140(1)499,
150(1)87,
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152(1)347,
157(2)329,
159(2)217,
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126(1)381,
130(1)197,
136(1)17,
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154(1)175,
161(1)179,
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169(1)127,
169(1)183
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116(2)221,
125(1)385,
134(1)165,
146(2)323
- convolution,
115(1)301,
145(1)183,
153(1)191
- dimensional,
115(1)301,
132(1)15,
134(1)259,
143(1)9,
144(1)131,
166(2)385,
169(2)247
- dimensional, multi-,
147(2)385,
155(2)423
- dimensional, one-,
114(1)103,
114(2)275,
125(1)395,
132(2)431,
145(1)31,
145(2)525,
146(1)11,
147(2)301,
152(1)367,
171(1)247
- evaluating,
131(1)223,
146(2)231,
149(2)381,
166(2)581
- explicit,
140(1)231,
140(1)559,
143(1)69,
147(1)75,
149(2)407,
152(1)187,
154(1)27,
155(1)187,
156(2)319,
160(1)37,
161(2)283,
167(1)1,
168(1)331,
169(1)171
- formula,
115(1)269,
115(1)471,
115(1)565,
118(1)125,
126(1)269,
126(1)287,
127(1)153,
127(1)201,
131(1)65,
132(1)1,
132(1)15,
133(1)151,
135(2)293,
135(2)313,
136(1)99,
138(2)259,
139(1)65,
140(1)291,
150(1)25,
154(2)355,
160(1)297,
161(2)431,
167(1)219,
169(2)419
- given,
113(1)73,
123(1)117,
140(1)837,
164(z)783
- indefinite,
161(2)431,
171(1)93
- initial,
115(1)495,
115(1)593,
125(1)31,
125(1)41,
125(1)117,
130(1)173,
134(1)165
- integral,
89(2)257,
113(1)35,
115(1)93,
115(1)193,
115(1)245,
115(1)269,
115(1)283,
115(1)433,
115(1)503,
116(1)23,
118(1)151,
118(1)223,
118(1)301,
118(1)311,
118(1)353,
121(1)113,
125(1)xi--xviii,
125(1)395,
125(1)423,
125(1)521,
126(1)207,
126(1)221,
130(1)323,
131(1)223,
131(1)267,
132(2)387,
132(2)409,
134(1)1,
134(1)23,
134(1)113,
134(1)201,
134(1)259,
135(2)303,
135(2)313,
136(1)149,
138(2)273,
139(1)49,
139(2)275,
140(1)381,
140(1)537,
140(1)587,
142(2)435,
142(2)449,
145(2)335,
146(2)231,
146(2)343,
147(1)1,
147(1)99,
148(2)363,
149(1)351,
149(2)381,
149(2)469,
150(1)157,
153(1)331,
154(2)431,
156(2)265,
156(2)471,
157(1)31,
157(1)93,
157(1)187,
158(2)355,
159(2)205,
159(2)285,
160(1)125,
160(1)159,
160(1)265,
161(1)145,
161(1)161,
163(2)401,
164(z)225,
164(z)307,
164(z)337,
164(z)431,
167(2)293,
167(2)321,
168(1)471,
169(2)247,
171(1)103,
171(1)141,
172(2)233,
172(2)289,
176(2)259
- integration,
115(1)121,
115(1)495,
115(1)503,
116(2)275,
126(1)381,
128(1)399,
131(1)195,
131(1)493,
133(1)611,
138(1)51,
139(1)1,
145(2)345,
149(1)1,
150(2)283,
151(1)141,
152(1)493,
154(1)229,
157(2)309,
158(1)75,
159(1)119,
161(2)283,
161(2)431,
163(1)59,
166(2)477,
172(2)247
- list,
133(1)xv--xviii,
133(1)xix--xxvii
- multi-dimensional,
147(2)385,
155(2)423
- one,
133(1)455,
138(2)325,
140(1)773,
146(1)99,
149(2)423,
150(2)375
- one-dimensional,
114(1)103,
114(2)275,
125(1)395,
132(2)431,
145(1)31,
145(2)525,
146(1)11,
147(2)301,
152(1)367,
171(1)247
- ordinary,
115(1)495,
125(1)xi--xviii,
125(1)1,
128(1)399,
133(1)85,
156(2)355,
158(2)397,
167(2)389,
169(1)171,
169(1)235
- partial,
114(1)173,
115(1)137,
128(1)ix--xi,
128(1)1,
128(1)55,
128(1)205,
128(1)399,
128(1)423,
128(1)447,
132(2)479,
141(1)35,
143(1)9,
147(2)349,
154(2)373,
163(1)29,
163(1)211,
166(1)181,
170(1)27
- result,
113(1)1,
113(1)123,
113(1)141,
113(1)211,
113(1)241,
131(1)55,
133(1)65,
135(2)325,
141(1)237,
142(2)445,
143(1)69,
145(2)269,
153(1)355,
154(1)183,
157(2)407,
161(2)313,
161(2)339,
166(2)525,
167(2)493,
169(1)45,
170(2)291,
171(1)93,
171(1)113
- Sinc,
130(1)283,
137(2)245,
164(z)673
- space,
113(1)183,
113(1)267,
113(1)283,
116(1)23,
118(1)151,
119(1)13,
119(1)209,
119(1)347,
119(1)377,
121(1)1,
121(1)165,
130(1)369,
133(1)601,
133(1)657,
137(2)363,
139(2)299,
144(1)175,
144(1)241,
144(1)291,
147(2)369,
147(2)485,
149(2)397,
153(1)99,
155(1)187,
157(2)261,
157(2)419,
159(2)249,
162(1)93,
162(2)365,
164(z)365,
166(1)209,
171(1)39
- starting,
129(1)151,
140(1)345,
169(2)333
- summary,
128(1)423
- survey,
122(1)167,
124(1)45,
134(1)325,
136(1)283,
140(1)331,
141(1)1,
144(1)7,
162(1)133,
164(z)587
- technique,
122(1)37,
132(2)309,
136(1)73,
140(1)245,
140(1)849,
152(1)199,
166(1)267,
168(1)353,
168(1)481,
170(2)337
- theory,
113(1)141,
113(1)195,
114(1)81,
120(1)109,
121(1)ix--x,
121(1)165,
121(1)313,
121(1)331,
121(1)421,
124(1)25,
130(1)17,
135(2)241,
137(1)49,
141(1)197,
143(1)81,
144(1)1,
148(1)307,
151(1)119,
153(1)521,
156(1)1,
159(2)285,
161(2)477,
167(2)255,
170(2)291,
170(2)317,
171(1)1,
171(1)113,
171(1)151,
171(1)235,
171(1)265,
171(1)411
- use,
116(1)93,
123(1)117,
133(1)111,
150(2)375,
152(1)199,
167(2)293,
167(2)321
- v,
168(1)235
- value,
113(1)27,
113(1)227,
113(1)267,
113(1)317,
113(1)381,
115(1)495,
115(1)519,
116(1)121,
116(2)231,
125(1)31,
125(1)41,
125(1)117,
126(1)145,
130(1)41,
132(1)107,
132(2)247,
132(2)399,
134(1)85,
134(1)165,
136(1)189,
136(1)259,
136(1)337,
138(1)173,
138(2)205,
139(1)9,
140(1)185,
141(1)27,
141(1)57,
141(1)65,
141(1)75,
141(1)117,
141(1)123,
141(1)237,
142(2)331,
143(1)107,
143(2)275,
145(1)89,
146(2)405,
147(1)41,
148(1)29,
148(1)307,
148(2)341,
149(1)239,
151(2)415,
152(1)161,
152(1)427,
153(1)201,
155(2)339,
156(1)239,
156(2)471,
158(2)339,
160(1)265,
160(1)323,
162(1)133,
166(1)221,
166(2)553,
169(1)183,
169(2)345,
170(1)145,
170(1)197