Approximating Integrals via Monte Carlo and Deterministic Methods

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OUP Oxford, Mar 23, 2000 - Mathematics - 298 pages
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This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.
 

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Contents

I
1
II
4
III
7
IV
13
V
15
VI
17
VII
18
VIII
19
XXVIII
101
XXIX
117
XXX
124
XXXI
132
XXXII
137
XXXIII
143
XXXIV
152
XXXV
156

IX
21
X
22
XI
27
XII
28
XIII
30
XIV
31
XV
36
XVI
38
XVII
40
XVIII
41
XIX
47
XX
49
XXI
52
XXII
54
XXIII
55
XXIV
57
XXV
86
XXVI
95
XXVII
97
XXXVI
161
XXXVII
165
XXXVIII
166
XXXIX
175
XL
182
XLI
209
XLII
221
XLIII
225
XLIV
226
XLV
232
XLVI
248
XLVII
257
XLVIII
263
XLIX
264
L
266
LI
281
LII
285
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