Numerical Computation 1: Methods, Software, and AnalysisThis 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. |
Contents
I | 1 |
II | 3 |
IV | 4 |
V | 5 |
VIII | 6 |
IX | 8 |
XI | 9 |
XII | 10 |
CLIV | 233 |
CLV | 234 |
CLVI | 235 |
CLVII | 236 |
CLVIII | 238 |
CLIX | 243 |
CLX | 246 |
CLXI | 247 |
XIII | 14 |
XIV | 16 |
XV | 19 |
XVI | 21 |
XVII | 23 |
XVIII | 28 |
XIX | 29 |
XXI | 30 |
XXII | 34 |
XXIII | 37 |
XXIV | 39 |
XXVII | 40 |
XXVIII | 42 |
XXX | 43 |
XXXI | 44 |
XXXII | 45 |
XXXIII | 46 |
XXXIV | 48 |
XXXVI | 54 |
XXXVII | 58 |
XXXIX | 59 |
XL | 60 |
XLI | 65 |
XLII | 68 |
XLIII | 70 |
XLIV | 71 |
XLV | 75 |
XLVII | 77 |
XLVIII | 78 |
XLIX | 79 |
L | 81 |
LI | 82 |
LII | 83 |
LIII | 88 |
LIV | 89 |
LV | 90 |
LVI | 91 |
LVII | 92 |
LVIII | 94 |
LX | 95 |
LXI | 97 |
LXII | 100 |
LXIII | 101 |
LXVI | 102 |
LXVII | 104 |
LXVIII | 106 |
LXIX | 107 |
LXX | 108 |
LXXII | 110 |
LXXV | 111 |
LXXVII | 112 |
LXXVIII | 113 |
LXXIX | 116 |
LXXX | 117 |
LXXXI | 118 |
LXXXII | 120 |
LXXXIII | 122 |
LXXXIV | 126 |
LXXXVI | 127 |
LXXXVII | 128 |
LXXXVIII | 129 |
LXXXIX | 131 |
XC | 132 |
XCII | 134 |
XCV | 135 |
XCVI | 136 |
XCVII | 139 |
XCVIII | 142 |
XCIX | 146 |
C | 147 |
CI | 151 |
CIII | 152 |
CIV | 154 |
CV | 155 |
CVI | 156 |
CVIII | 159 |
CIX | 162 |
CX | 163 |
CXI | 164 |
CXIII | 165 |
CXIV | 167 |
CXV | 171 |
CXVI | 172 |
CXVII | 174 |
CXVIII | 175 |
CXXII | 177 |
CXXIV | 178 |
CXXV | 179 |
CXXVII | 181 |
CXXIX | 183 |
CXXX | 184 |
CXXXI | 185 |
CXXXII | 186 |
CXXXIII | 187 |
CXXXIV | 191 |
CXXXV | 194 |
CXXXVII | 195 |
CXXXVIII | 196 |
CXL | 199 |
CXLI | 200 |
CXLII | 201 |
CXLIII | 210 |
CXLIV | 212 |
CXLV | 213 |
CXLVI | 214 |
CXLVII | 215 |
CXLVIII | 219 |
CXLIX | 224 |
CL | 226 |
CLI | 229 |
CLIII | 232 |
CLXII | 248 |
CLXIII | 249 |
CLXV | 252 |
CLXVI | 253 |
CLXVII | 254 |
CLXVIII | 256 |
CLXIX | 257 |
CLXX | 258 |
CLXXI | 261 |
CLXXII | 262 |
CLXXIII | 263 |
CLXXIV | 264 |
CLXXV | 266 |
CLXXVI | 267 |
CLXXVII | 269 |
CLXXVIII | 272 |
CLXXIX | 274 |
CLXXXI | 275 |
CLXXXII | 276 |
CLXXXIII | 278 |
CLXXXIV | 280 |
CLXXXV | 281 |
CLXXXVI | 282 |
CLXXXVII | 284 |
CLXXXVIII | 285 |
CXC | 291 |
CXCI | 292 |
CXCII | 293 |
CXCIII | 295 |
CXCVII | 296 |
CXCVIII | 297 |
CC | 298 |
CCI | 299 |
CCII | 300 |
CCIII | 301 |
CCIV | 302 |
CCV | 305 |
CCVI | 306 |
CCVII | 308 |
CCVIII | 309 |
CCIX | 311 |
CCX | 312 |
CCXIII | 314 |
CCXIV | 316 |
CCXV | 317 |
CCXVII | 319 |
CCXIX | 321 |
CCXX | 322 |
CCXXII | 323 |
CCXXIII | 325 |
CCXXIV | 326 |
CCXXVI | 327 |
CCXXVII | 329 |
CCXXVIII | 330 |
CCXXIX | 332 |
CCXXX | 333 |
CCXXXI | 334 |
CCXXXII | 335 |
CCXXXIII | 337 |
CCXXXIV | 339 |
CCXXXVI | 341 |
CCXXXVII | 343 |
CCXXXIX | 344 |
CCXLI | 347 |
CCXLII | 350 |
CCXLIV | 351 |
CCXLV | 353 |
CCXLVII | 354 |
CCXLIX | 355 |
CCL | 356 |
CCLII | 360 |
CCLIII | 361 |
CCLV | 362 |
CCLVI | 367 |
CCLVII | 369 |
CCLVIII | 373 |
CCLIX | 374 |
CCLX | 377 |
CCLXI | 386 |
CCLXII | 390 |
CCLXIII | 393 |
CCLXIV | 394 |
CCLXV | 396 |
CCLXVI | 397 |
CCLXVIII | 399 |
CCLXIX | 401 |
CCLXX | 403 |
CCLXXI | 406 |
CCLXXII | 407 |
CCLXXIII | 411 |
CCLXXIV | 412 |
CCLXXV | 413 |
CCLXXVI | 414 |
CCLXXVII | 415 |
CCLXXIX | 416 |
CCLXXXI | 419 |
CCLXXXII | 421 |
CCLXXXIII | 422 |
CCLXXXIV | 426 |
CCLXXXV | 429 |
CCLXXXVI | 430 |
CCLXXXVII | 431 |
CCLXXXVIII | 433 |
CCLXXXIX | 435 |
CCXC | 437 |
CCXCII | 438 |
CCXCIII | 440 |
443 | |
460 | |
466 | |
Other editions - View all
Numerical Computation 1: Methods, Software, and Analysis Christoph W. Ueberhuber Limited preview - 2012 |
Common terms and phrases
accuracy algebraic approximating function arithmetic operations B-spline binary cache calculated Chebyshev Chebyshev nodes Chebyshev polynomials coefficients complexity computational effort condition number cubic spline cubic spline function data points defined degree denormalized depends derivative determined digits discrete efficiency END DO END evaluation exact Example execution exponent finite floating-point number system floating-point operations floating-point performance Fortran 90 function f function values given hardware IEC/IEEE implementation instructions integration intermediate results Internet interpolation function interpolation nodes interpolation polynomial interval LAPACK linear equations LINPACK locality of reference loop unrolling main memory mantissa mathematical problem matrix memory hierarchy method Mflop/s model function NETLIB nonlinear norm numerical data processing numerical software obtained operands optimal oscillation parameters perturbations piecewise pipeline polynomial interpolation possible precision processor real numbers representation rounding error Section sequence solution solve specified Strassen algorithm subroutine summation system of linear theorem transformations vector vector processors workstation zero
References to this book
Numerical Computing with IEEE Floating Point Arithmetic Michael L. Overton No preview available - 2001 |