This book examines the solution of some of the most common problems of numerical computation. By concentrating on one effective algorithm for each basic task, it develops the fundamental theory in a brief, elementary way. There are ample exercises, and codes are provided to reduce the time otherwise required for programming and debugging. Exposes readers to art of numerical computing as well as the science. Readers need only a familiarity with either FORTRAN or C. Applications are taken from a variety of disciplines including engineering, physics, and chemistry.
Author(s): L. F. Shampine, Rebecca Chan Allen, S. Pruess
Publisher: John Wiley
Year: 1997
Language: English
Pages: 279
City: New York
PRELIMINARIES......Page 4
CONTENTS......Page 8
1.1 BASIC CONCEPTS......Page 10
EXERCISES......Page 20
1.2 EXAMPLES OF FLOATING POINT CALCULATIONS......Page 21
EXERCISES......Page 32
1.3 CASE STUDY 1......Page 34
REFERENCES......Page 37
MISCELLANEOUS EXERCISES FOR CHAPTER 1......Page 38
SYSTEMS OF LINEAR EQUATIONS......Page 39
2.1 GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING......Page 41
EXERCISES......Page 51
2.2 MATRIX FACTORIZATION......Page 53
2.3 ACCURACY......Page 57
A BACKWARD ERROR ANALYSIS......Page 58
ROUNDOFF ANALYSIS......Page 60
OTHER ERROR EXPRESSIONS AND APPROXIMATIONS......Page 67
ESTIMATING CONDITION......Page 68
2.4 ROUTINES FACTOR AND SOLVE......Page 70
EXERCISES......Page 72
2.5 MATRICES WITH SPECIAL STRUCTURE......Page 74
2.6 CASE STUDY 2......Page 81
REFERENCES......Page 87
MISCELLANEOUS EXERCISES FOR CHAPTER 2......Page 88
INTERPOLATION......Page 91
3.1 POLYNOMIAL INTERPOLATION......Page 92
EXERCISES......Page 98
3.2 MORE ERROR BOUNDS......Page 99
3.3 NEWTON DIVIDED DIFFERENCE FORM......Page 102
3.4 ASSESSING ACCURACY......Page 107
3.5 SPLINE INTERPOLATION......Page 110
EXERCISES......Page 125
3.6 INTERPOLATION IN THE PLANE......Page 130
EXERCISES......Page 138
3.7 CASE STUDY 3......Page 139
REFERENCES......Page 142
MISCELLANEOUS EXERCISES FOR CHAPTER 3......Page 143
ROOTS OF NONLINEAR EQUATIONS......Page 145
4.1 BISECTION, NEWTON’S METHOD, AND THE SECANT RULE......Page 148
EXERCISES......Page 160
4.2 AN ALGORITHM COMBINING BISECTION AND THE SECANT RULE......Page 161
4.3 ROUTINES FOR ZERO FINDING......Page 163
EXERCISES......Page 166
4.4 CONDITION, LIMITING PRECISION, AND MULTIPLE ROOTS......Page 168
4.5 NONLINEAR SYSTEMS OF EQUATIONS......Page 171
EXERCISES......Page 173
4.6 CASE STUDY 4......Page 174
MISCELLANEOUS EXERCISES FOR CHAPTER 4......Page 178
5.1 BASIC QUADRATURE RULES......Page 181
5.2 ADAPTIVE QUADRATURE......Page 195
5.3 CODES FOR ADAPTIVE QUADRATURE......Page 199
EXERCISES......Page 200
5.4 SPECIAL DEVICES FOR INTEGRATION......Page 202
OSCILLATORY INTEGRANDS......Page 203
SINGULAR INTEGRANDS......Page 204
EXERCISES......Page 209
5.5 INTEGRATION OF TABULAR DATA......Page 211
EXERCISES......Page 212
5.6 INTEGRATION IN TWO VARIABLES......Page 213
5.7 CASE STUDY 5......Page 214
REFERENCES......Page 218
EXERCISES......Page 219
6.1 SOME ELEMENTS OF THE THEORY......Page 221
6.2 A SIMPLE NUMERICAL SCHEME......Page 227
6.3 ONE- STEP METHODS......Page 232
EXERCISES......Page 238
6.4 ERRORS- LOCAL AND GLOBAL......Page 239
6.5 THE ALGORITHMS......Page 244
EXERCISES......Page 246
6.6 THE CODE RKE......Page 247
EXERCISES......Page 249
6.7 OTHER NUMERICAL METHODS......Page 251
6.8 CASE STUDY 6......Page 255
REFERENCES......Page 259
MISCELLANEOUS EXERCISES FOR CHAPTER 6......Page 260
A. 1 NOTATION......Page 262
A. 2 THEOREMS......Page 263
ANSWERS TO SELECTED EXERCISES......Page 266
INDEX......Page 277
