Numerical Computation 1: Methods, Software, and Analysis

Front Cover
Springer Science & Business Media, Feb 27, 1997 - Mathematics - 474 pages
This book deals with various aspects of scientific numerical computing. No at tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.
 

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Contents

I
1
II
3
IV
4
V
5
VIII
6
IX
8
X
9
XI
10
CXLIII
233
CXLIV
234
CXLV
235
CXLVI
236
CXLVII
238
CXLVIII
243
CXLIX
246
CL
247

XII
14
XIII
16
XIV
19
XV
21
XVI
23
XVII
28
XVIII
29
XX
30
XXI
34
XXII
37
XXIII
39
XXV
40
XXVI
42
XXVII
43
XXVIII
44
XXIX
45
XXX
46
XXXI
48
XXXIII
54
XXXIV
58
XXXVI
59
XXXVII
60
XXXVIII
65
XXXIX
68
XL
70
XLI
71
XLII
75
XLIII
77
XLIV
78
XLV
79
XLVI
81
XLVII
82
XLVIII
83
XLIX
88
L
89
LI
90
LII
91
LIII
92
LIV
94
LVI
95
LVII
97
LVIII
100
LIX
101
LX
102
LXI
104
LXII
106
LXVIII
107
LXIX
108
LXX
110
LXXI
111
LXXIII
112
LXXIV
113
LXXV
116
LXXVI
117
LXXVII
118
LXXVIII
120
LXXIX
122
LXXX
126
LXXXI
127
LXXXII
128
LXXXIII
129
LXXXIV
131
LXXXV
132
LXXXVI
134
LXXXVII
135
LXXXVIII
136
LXXXIX
139
XC
142
XCI
146
XCII
147
XCIII
151
XCV
152
XCVI
154
XCVII
155
XCVIII
156
XCIX
159
C
162
CI
163
CII
164
CIII
165
CIV
167
CV
171
CVI
172
CVII
174
CVIII
175
CXII
177
CXIII
178
CXIV
179
CXVI
181
CXVIII
183
CXIX
184
CXX
185
CXXI
186
CXXII
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CXXIII
191
CXXIV
194
CXXVI
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CXXVII
196
CXXIX
199
CXXX
200
CXXXI
201
CXXXII
210
CXXXIII
212
CXXXIV
213
CXXXV
214
CXXXVI
215
CXXXVII
219
CXXXVIII
224
CXXXIX
226
CXL
229
CXLII
232
CLI
248
CLII
249
CLIII
252
CLIV
253
CLV
254
CLVI
256
CLVII
257
CLVIII
258
CLIX
261
CLX
262
CLXI
263
CLXII
264
CLXIII
266
CLXIV
267
CLXV
269
CLXVI
272
CLXVII
274
CLXVIII
275
CLXIX
276
CLXX
278
CLXXI
280
CLXXII
281
CLXXIII
282
CLXXIV
284
CLXXV
285
CLXXVI
291
CLXXVII
292
CLXXVIII
293
CLXXIX
295
CLXXXIII
296
CLXXXIV
297
CLXXXV
298
CLXXXVI
299
CLXXXVII
300
CLXXXVIII
301
CLXXXIX
302
CXC
305
CXCI
306
CXCII
308
CXCIII
309
CXCIV
311
CXCV
312
CXCVIII
314
CXCIX
316
CC
317
CCII
319
CCIII
321
CCIV
322
CCV
323
CCVI
325
CCVII
326
CCVIII
327
CCIX
329
CCX
330
CCXI
332
CCXII
333
CCXIII
334
CCXIV
335
CCXV
337
CCXVI
339
CCXVIII
341
CCXIX
343
CCXXI
344
CCXXII
347
CCXXIII
350
CCXXV
351
CCXXVI
353
CCXXVIII
354
CCXXX
355
CCXXXI
356
CCXXXIII
360
CCXXXIV
361
CCXXXVI
362
CCXXXVII
367
CCXXXVIII
369
CCXXXIX
373
CCXL
374
CCXLI
377
CCXLII
386
CCXLIII
390
CCXLIV
393
CCXLV
394
CCXLVI
396
CCXLVII
397
CCXLIX
399
CCL
401
CCLI
403
CCLII
406
CCLIII
407
CCLIV
411
CCLV
412
CCLVI
413
CCLVII
414
CCLVIII
415
CCLX
416
CCLXI
419
CCLXII
421
CCLXIII
422
CCLXIV
426
CCLXV
429
CCLXVI
430
CCLXVII
431
CCLXVIII
433
CCLXIX
435
CCLXX
437
CCLXXI
438
CCLXXII
440
CCLXXIII
443
CCLXXIV
460
CCLXXV
466
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