Numerical recipes

Recommendations

Info

730 Chapter 16. Integration of Ordinary Differential Equations } if (k == kmax || k == kopt+1) { Check for possible stepsize red=SAFE2/err[km]; reduction. break; } else if (k == kopt && alf[kopt-1][kopt] < err[km]) { red=1.0/err[km]; break; } else if (kopt == kmax && alf[km][kmax-1] < err[km]) { red=alf[km][kmax-1]*SAFE2/err[km]; break; } else if (alf[km][kopt] < err[km]) { red=alf[km][kopt-1]/err[km]; break; } } } if (exitflag) break; red=FMIN(red,REDMIN); Reduce stepsize by at least REDMIN red=FMAX(red,REDMAX); and at most REDMAX. h *= red; reduct=1; } Try again. *xx=xnew; Successful step taken. *hdid=h; first=0; wrkmin=1.0e35; Compute optimal row for convergence for (kk=1;kk= k && kopt != kmax && !reduct) { Check for possible order increase, but not if stepsize was just reduced. fact=FMAX(scale/alf[kopt-1][kopt],SCALMX); if (a[kopt+1]*fact
16.4 Richardson Extrapolation and the Bulirsch-Stoer Method 731 #include "nrutil.h" extern float **d,*x; Defined in bsstep. void pzextr(int iest, float xest, float yest[], float yz[], float dy[], int nv) Use polynomial extrapolation to evaluate nv functions at x =0by fitting a polynomial to a sequence of estimates with progressively smaller values x = xest, and corresponding function vectors yest[1..nv]. This call is number iest in the sequence of calls. Extrapolated function values are output as yz[1..nv], and their estimated error is output as dy[1..nv]. { int k1,j; float q,f2,f1,delta,*c; } c=vector(1,nv); x[iest]=xest; Save current independent variable. for (j=1;j
Page 1 and 2:
Numerical Recipes in C The Art of S
Page 3 and 4:
Contents Preface to the Second Edit
Page 5 and 6:
Contents vii 7.2 Transformation Met
Page 7 and 8:
Contents ix 15.6 Confidence Limits
Page 9 and 10:
Preface to the Second Edition Our a
Page 11 and 12:
Preface to the Second Edition xiii
Page 13 and 14:
Preface to the First Edition xv lin
Page 15 and 16:
Types of License Offered License In
Page 17 and 18:
Computer Programs by Chapter and Se
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Chapter 1. Preliminaries 1.0 Introd
Page 27 and 28:
1.0 Introduction 3 Tested Machines
Page 29 and 30:
1.1 Program Organization and Contro
Page 31 and 32:
Page 33 and 34:
true 1.1 Program Organization and C
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
} 1.2 Some C Conventions for Scient
Page 41 and 42:
1.2 Some C Conventions for Scientif
Page 43 and 44:
Page 45 and 46:
(a) **m (b) **m 1.2 Some C Conventi
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
= 0 3 = 0 = 0 = 0 = 0 = 0 1 ⁄ 2 1
Page 55 and 56:
1.3 Error, Accuracy, and Stability
Page 57 and 58:
2.0 Introduction 33 Accumulated rou
Page 59 and 60:
2.0 Introduction 35 between singula
Page 61 and 62:
2.1 Gauss-Jordan Elimination 37 Eli
Page 63 and 64:
2.1 Gauss-Jordan Elimination 39 pre
Page 65 and 66:
2.2 Gaussian Elimination with Backs
Page 67 and 68:
2.3 LU Decomposition and Its Applic
Page 69 and 70:
a b c d 2.3 LU Decomposition and It
Page 71 and 72:
} 2.3 LU Decomposition and Its Appl
Page 73 and 74:
2.3 LU Decomposition and Its Applic
Page 75 and 76:
2.4 Tridiagonal and Band Diagonal S
Page 77 and 78:
2.4 Tridiagonal and Band Diagonal S
Page 79 and 80:
δx 2.5 Iterative Improvement of a
Page 81 and 82:
2.5 Iterative Improvement of a Solu
Page 83 and 84:
2.6 Singular Value Decomposition 59
Page 85 and 86:
SVD of a Square Matrix 2.6 Singular
Page 87 and 88:
solutions of A ⋅ x = d null space
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
} 2.6 Singular Value Decomposition
Page 95 and 96:
2.7 Sparse Linear Systems 2.7 Spars
Page 97 and 98:
2.7 Sparse Linear Systems 73 prescr
Page 99 and 100:
2.7 Sparse Linear Systems 75 Here
Page 101 and 102:
2.7 Sparse Linear Systems 77 Finall
Page 103 and 104:
2.7 Sparse Linear Systems 79 In row
Page 105 and 106:
} 2.7 Sparse Linear Systems 81 jp=i
Page 107 and 108:
2.7 Sparse Linear Systems 83 Matrix
Page 109 and 110:
2.7 Sparse Linear Systems 85 while
Page 111 and 112:
p=dvector(1,n); pp=dvector(1,n); r=
Page 113 and 114:
} 2.7 Sparse Linear Systems 89 void
Page 115 and 116:
2.8 Vandermonde Matrices and Toepli
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
2.9 Cholesky Decomposition 97 If yo
Page 123 and 124:
2.10 QR Decomposition 99 The standa
Page 125 and 126:
#include #include "nrutil.h" 2.10
Page 127 and 128:
in terms of which 2.11 Is Matrix In
Page 129 and 130:
Chapter 3. Interpolation and Extrap
Page 131 and 132:
(a) (b) 3.0 Introduction 107 Figure
Page 133 and 134:
3.1 Polynomial Interpolation and Ex
Page 135 and 136:
3.2 Rational Function Interpolation
Page 137 and 138:
3.3 Cubic Spline Interpolation 113
Page 139 and 140:
3.3 Cubic Spline Interpolation 115
Page 141 and 142:
3.4 How to Search an Ordered Table
Page 143 and 144:
} 3.4 How to Search an Ordered Tabl
Page 145 and 146:
#include "nrutil.h" 3.5 Coefficient
Page 147 and 148:
3.6 Interpolation in Two or More Di
Page 149 and 150:
} int j; float *ymtmp; 3.6 Interpol
Page 151 and 152:
3.6 Interpolation in Two or More Di
Page 153 and 154:
Chapter 4. Integration of Functions
Page 155 and 156:
4.1 Classical Formulas for Equally
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
#define FUNC(x) ((*func)(x)) 4.2 El
Page 163 and 164:
4.2 Elementary Algorithms 139 trapz
Page 165 and 166:
4.4 Improper Integrals 141 which co
Page 167 and 168:
4.4 Improper Integrals 143 The rout
Page 169 and 170:
4.4 Improper Integrals 145 If you n
Page 171 and 172:
4.5 Gaussian Quadratures and Orthog
Page 173 and 174:
Page 175 and 176:
Gauss-Legendre: Gauss-Chebyshev: Ga
Page 177 and 178:
} 4.5 Gaussian Quadratures and Orth
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
4.6 Multidimensional Integrals 161
Page 187 and 188:
y 4.6 Multidimensional Integrals 16
Page 189 and 190:
Chapter 5. Evaluation of Functions
Page 191 and 192:
5.1 Series and Their Convergence 16
Page 193 and 194:
5.2 Evaluation of Continued Fractio
Page 195 and 196:
5.2 Evaluation of Continued Fractio
Page 197 and 198:
5.3 Polynomials and Rational Functi
Page 199 and 200:
5.3 Polynomials and Rational Functi
Page 201 and 202:
5.4 Complex Arithmetic 177 Actually
Page 203 and 204:
5.5 Recurrence Relations and Clensh
Page 205 and 206:
5.5 Recurrence Relations and Clensh
Page 207 and 208:
5.6 Quadratic and Cubic Equations 1
Page 209 and 210:
5.6 Quadratic and Cubic Equations 1
Page 211 and 212:
5.7 Numerical Derivatives 187 With
Page 213 and 214:
} 5.7 Numerical Derivatives 189 The
Page 215 and 216:
Chebyshev polynomials 1 .5 0 −.5
Page 217 and 218:
} 5.8 Chebyshev Approximation 193 f
Page 219 and 220:
5.9 Derivatives or Integrals of a C
Page 221 and 222:
5.10 Polynomial Approximation from
Page 223 and 224:
5.11 Economization of Power Series
Page 225 and 226:
5.12 Padé Approximants 201 then R(
Page 227 and 228:
5.12 Padé Approximants 203 cof[2*n
Page 229 and 230:
5.13 Rational Chebyshev Approximati
Page 231 and 232:
5.13 Rational Chebyshev Approximati
Page 233 and 234:
5.14 Evaluation of Functions by Pat
Page 235 and 236:
5.14 Evaluation of Functions by Pat
Page 237 and 238:
6.1 Gamma, Beta, and Related Functi
Page 239 and 240:
6.1 Gamma, Beta, and Related Functi
Page 241 and 242:
incomplete gamma function P(a,x) 1.
Page 243 and 244:
} void nrerror(char error_text[]);
Page 245 and 246:
#include 6.2 Incomplete Gamma Func
Page 247 and 248:
6.3 Exponential Integrals 223 where
Page 249 and 250:
6.3 Exponential Integrals 225 #incl
Page 251 and 252:
6.4 Incomplete Beta Function 227 Th
Page 253 and 254:
6.4 Incomplete Beta Function 229 So
Page 255 and 256:
Bessel functions 1 .5 0 −.5 −1
Page 257 and 258:
} 6.5 Bessel Functions of Integer O
Page 259 and 260:
6.5 Bessel Functions of Integer Ord
Page 261 and 262:
modified Bessel functions 4 3 2 1 6
Page 263 and 264:
6.6 Modified Bessel Functions of In
Page 265 and 266:
6.7 Bessel Functions of Fractional
Page 267 and 268:
Page 269 and 270:
} 6.7 Bessel Functions of Fractiona
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
6.8 Spherical Harmonics 253 The fir
Page 279 and 280:
6.9 Fresnel Integrals, Cosine and S
Page 281 and 282:
} 6.9 Fresnel Integrals, Cosine and
Page 283 and 284:
} 6.10 Dawson’s Integral 259 } if
Page 285 and 286:
6.11 Elliptic Integrals and Jacobia
Page 287 and 288:
where 6.11 Elliptic Integrals and J
Page 289 and 290:
#define TINY 1.0e-25 #define BIG 4.
Page 291 and 292:
6.11 Elliptic Integrals and Jacobia
Page 293 and 294:
Page 295 and 296:
6.12 Hypergeometric Functions 271 C
Page 297 and 298:
#include "complex.h" #define ONE Co
Page 299 and 300:
7.1 Uniform Deviates 275 As for ref
Page 301 and 302:
7.1 Uniform Deviates 277 This corre
Page 303 and 304:
#define IA 16807 #define IM 2147483
Page 305 and 306:
RAN 3 1 7.1 Uniform Deviates 281 iy
Page 307 and 308:
7.1 Uniform Deviates 283 from the w
Page 309 and 310:
7.1 Uniform Deviates 285 Constants
Page 311 and 312:
7.2 Transformation Method: Exponent
Page 313 and 314:
7.2 Transformation Method: Exponent
Page 315 and 316:
first random deviate in 7.3 Rejecti
Page 317 and 318:
} 7.3 Rejection Method: Gamma, Pois
Page 319 and 320:
} 7.3 Rejection Method: Gamma, Pois
Page 321 and 322:
7.4 Generation of Random Bits 297 s
Page 323 and 324:
} } *iseed
Page 325 and 326:
7.5 Random Sequences Based on Data
Page 327 and 328:
} } 7.5 Random Sequences Based on D
Page 329 and 330:
7.6 Simple Monte Carlo Integration
Page 331 and 332:
7.6 Simple Monte Carlo Integration
Page 333 and 334:
7.7 Quasi- (that is, Sub-) Random S
Page 335 and 336:
Page 337 and 338:
} 7.7 Quasi- (that is, Sub-) Random
Page 339 and 340:
Page 341 and 342:
7.8 Adaptive and Recursive Monte Ca
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
} } 7.8 Adaptive and Recursive Mont
Page 349 and 350:
Page 351 and 352:
} 7.8 Adaptive and Recursive Monte
Page 353 and 354:
Chapter 8. Sorting 8.0 Introduction
Page 355 and 356:
8.1 Straight Insertion and Shell’
Page 357 and 358:
8.2 Quicksort 333 question of the b
Page 359 and 360:
8.2 Quicksort 335 istack=lvector(1,
Page 361 and 362:
a 4 a 2 8.3 Heapsort 337 a 5 a 1 a
Page 363 and 364:
original array 1 2 3 4 5 6 14 8 32
Page 365 and 366:
8.5 Selecting the Mth Largest 341 w
Page 367 and 368:
8.5 Selecting the Mth Largest 343 r
Page 369 and 370:
} } } } 8.6 Determination of Equiva
Page 371 and 372:
Chapter 9. Root Finding and Nonline
Page 373 and 374:
9.0 Introduction 349 good first gue
Page 375 and 376:
(a) (b) (c) (d) 9.1 Bracketing and
Page 377 and 378:
Bisection Method 9.1 Bracketing and
Page 379 and 380:
9.2 Secant Method, False Position M
Page 381 and 382:
} 9.2 Secant Method, False Position
Page 383 and 384:
} 9.3 Van Wijngaarden-Dekker-Brent
Page 385 and 386:
9.3 Van Wijngaarden-Dekker-Brent Me
Page 387 and 388:
9.4 Newton-Raphson Method Using Der
Page 389 and 390:
9.4 Newton-Raphson Method Using Der
Page 391 and 392:
} 9.4 Newton-Raphson Method Using D
Page 393 and 394:
9.5 Roots of Polynomials 9.5 Roots
Page 395 and 396:
9.5 Roots of Polynomials 371 tentat
Page 397 and 398:
9.5 Roots of Polynomials 373 The me
Page 399 and 400:
Eigenvalue Methods 9.5 Roots of Pol
Page 401 and 402:
9.5 Roots of Polynomials 377 of goi
Page 403 and 404:
9.6 Newton-Raphson Method for Nonli
Page 405 and 406:
9.6 Newton-Raphson Method for Nonli
Page 407 and 408:
9.7 Globally Convergent Methods for
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
Page 419 and 420:
X1 A B C 10.0 Introduction 395 D Fi
Page 421 and 422:
10.1 Golden Section Search in One D
Page 423 and 424:
10.1 Golden Section Search in One D
Page 425 and 426:
} } 10.1 Golden Section Search in O
Page 427 and 428:
10.2 Parabolic Interpolation and Br
Page 429 and 430:
} 10.3 One-Dimensional Search with
Page 431 and 432:
10.3 One-Dimensional Search with Fi
Page 433 and 434:
(a) (b) (c) (d) 10.4 Downhill Simpl
Page 435 and 436:
10.4 Downhill Simplex Method in Mul
Page 437 and 438:
10.5 Direction Set (Powell’s) Met
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
(a) 10.6 Conjugate Gradient Methods
Page 447 and 448:
10.6 Conjugate Gradient Methods in
Page 449 and 450:
} 10.7 Variable Metric Methods in M
Page 451 and 452:
10.7 Variable Metric Methods in Mul
Page 453 and 454:
} 10.7 Variable Metric Methods in M
Page 455 and 456:
10.8 Linear Programming and the Sim
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
} 10.8 Linear Programming and the S
Page 469 and 470:
10.9 Simulated Annealing Methods 44
Page 471 and 472:
(a) (b) (c) 1 .5 0 1 .5 0 1 .5 0 10
Page 473 and 474:
} } 10.9 Simulated Annealing Method
Page 475 and 476:
} free_ivector(jorder,1,ncity); #in
Page 477 and 478:
Page 479 and 480:
Page 481 and 482:
Definitions and Basic Facts 11.0 In
Page 483 and 484:
11.0 Introduction 459 In both the d
Page 485 and 486:
11.0 Introduction 461 “Eigenpacka
Page 487 and 488:
11.1 Jacobi Transformations of a Sy
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
} } 11.2 Reduction of a Symmetric M
Page 495 and 496:
11.2 Reduction of a Symmetric Matri
Page 497 and 498:
11.2 Reduction of a Symmetric Matri
Page 499 and 500:
11.3 Eigenvalues and Eigenvectors o
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
} } 11.4 Hermitian Matrices 481 for
Page 507 and 508:
11.5 Reduction of a General Matrix
Page 509 and 510:
11.5 Reduction of a General Matrix
Page 511 and 512:
11.6 The QR Algorithm for Real Hess
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
11.7 Eigenvalues or Eigenvectors by
Page 519 and 520:
11.7 Eigenvalues or Eigenvectors by
Page 521 and 522:
and equation (12.0.1) looks like th
Page 523 and 524:
⏐h(t)⏐ 2 (a) Ph( f ) (one-sided
Page 525 and 526:
12.1 Fourier Transform of Discretel
Page 527 and 528:
12.1 Fourier Transform of Discretel
Page 529 and 530:
12.2 Fast Fourier Transform (FFT) 5
Page 531 and 532:
12.2 Fast Fourier Transform (FFT) 5
Page 533 and 534:
Other FFT Algorithms 12.2 Fast Four
Page 535 and 536:
12.3 FFT of Real Functions, Sine an
Page 537 and 538:
12.3 FFT of Real Functions, Sine an
Page 539 and 540:
(a) (b) (c) +1 0 −1 +1 0 −1 +1
Page 541 and 542:
#include 12.3 FFT of Real Function
Page 543 and 544:
} 12.3 FFT of Real Functions, Sine
Page 545 and 546:
} } } 12.4 FFT in Two or More Dimen
Page 547 and 548:
data [1] Re Im 12.4 FFT in Two or M
Page 549 and 550:
12.5 Fourier Transforms of Real Dat
Page 551 and 552:
Page 553 and 554:
Page 555 and 556:
Page 557 and 558:
12.6 External Storage or Memory-Loc
Page 559 and 560:
} } 12.6 External Storage or Memory
Page 561 and 562:
Chapter 13. Fourier and Spectral Ap
Page 563 and 564:
(t) r*s(t) 13.1 Convolution and Dec
Page 565 and 566:
13.1 Convolution and Deconvolution
Page 567 and 568:
13.1 Convolution and Deconvolution
Page 569 and 570:
13.2 Correlation and Autocorrelatio
Page 571 and 572:
13.3 Optimal (Wiener) Filtering wit
Page 573 and 574:
log scale 13.4 Power Spectrum Estim
Page 575 and 576:
13.4 Power Spectrum Estimation Usin
Page 577 and 578:
Page 579 and 580:
amplitude 1 .8 .6 .4 .2 0 13.4 Powe
Page 581 and 582:
Page 583 and 584:
13.5 Digital Filtering in the Time
Page 585 and 586:
IIR (Recursive) Filters 13.5 Digita
Page 587 and 588:
(a) (b) 13.5 Digital Filtering in t
Page 589 and 590:
13.6 Linear Prediction and Linear P
Page 591 and 592:
Page 593 and 594:
} 13.6 Linear Prediction and Linear
Page 595 and 596:
Page 597 and 598:
13.7 Maximum Entropy (All Poles) Me
Page 599 and 600:
13.8 Spectral Analysis of Unevenly
Page 601 and 602:
Page 603 and 604:
Page 605 and 606:
} 13.8 Spectral Analysis of Unevenl
Page 607 and 608:
} 13.8 Spectral Analysis of Unevenl
Page 609 and 610:
13.9 Computing Fourier Integrals Us
Page 611 and 612:
Cubic order: 13.9 Computing Fourier
Page 613 and 614:
13.9 Computing Fourier Integrals Us
Page 615 and 616:
13.10 Wavelet Transforms 591 The sp
Page 617 and 618:
13.10 Wavelet Transforms 593 p.”
Page 619 and 620:
13.10 Wavelet Transforms 595 comple
Page 621 and 622:
} 13.10 Wavelet Transforms 597 wfil
Page 623 and 624:
.2 0 −.2 .2 0 −.2 DAUB4 e10 + e
Page 625 and 626:
wavelet amplitude 1.5 1 .5 .0001 10
Page 627 and 628:
} nprev=nnew; } free_vector(wksp,1,
Page 629 and 630:
13.10 Wavelet Transforms 605 Figure
Page 631 and 632:
13.11 Numerical Use of the Sampling
Page 633 and 634:
Chapter 14. Statistical Description
Page 635 and 636:
14.1 Moments of a Distribution: Mea
Page 637 and 638:
14.1 Moments of a Distribution: Mea
Page 639 and 640:
14.2 Do Two Distributions Have the
Page 641 and 642:
Page 643 and 644:
Page 645 and 646:
14.3 Are Two Distributions Differen
Page 647 and 648:
Page 649 and 650:
Page 651 and 652:
Page 653 and 654:
1. male 2. female . 14.4 Contingenc
Page 655 and 656:
14.4 Contingency Table Analysis of
Page 657 and 658:
Page 659 and 660:
Page 661 and 662:
14.5 Linear Correlation 637 two dis
Page 663 and 664:
14.6 Nonparametric or Rank Correlat
Page 665 and 666:
Page 667 and 668:
Page 669 and 670:
} } 14.7 Do Two-Dimensional Distrib
Page 671 and 672:
14.7 Do Two-Dimensional Distributio
Page 673 and 674:
Page 675 and 676:
14.8 Savitzky-Golay Smoothing Filte
Page 677 and 678:
8 6 4 2 0 8 6 4 2 0 8 6 4 2 0 befor
Page 679 and 680:
14.8 Savitzky-Golay Smoothing Filte
Page 681 and 682:
15.1 Least Squares as a Maximum Lik
Page 683 and 684:
15.1 Least Squares as a Maximum Lik
Page 685 and 686:
15.2 Fitting Data to a Straight Lin
Page 687 and 688:
15.2 Fitting Data to a Straight Lin
Page 689 and 690:
Page 691 and 692:
15.3 Straight-Line Data with Errors
Page 693 and 694:
15.3 Straight-Line Data with Errors
Page 695 and 696:
15.4 General Linear Least Squares 6
Page 697 and 698:
Page 699 and 700:
} 15.4 General Linear Least Squares
Page 701 and 702:
Page 703 and 704: 15.4 General Linear Least Squares 6
Page 705 and 706: 15.5 Nonlinear Models 681 Lawson, C
Page 707 and 708: 15.5 Nonlinear Models 683 Note that
Page 709 and 710: 15.5 Nonlinear Models 685 pivots, b
Page 711 and 712: #include "nrutil.h" 15.5 Nonlinear
Page 713 and 714: 15.6 Confidence Limits on Estimated
Page 715 and 716: actual data set 15.6 Confidence Lim
Page 723 and 724: 15.7 Robust Estimation 699 M� 1 C
Page 725 and 726: 15.7 Robust Estimation 701 where th
Page 727 and 728: 15.7 Robust Estimation 703 algorith
Page 729 and 730: } *a=aa; *b=bb; *abdev=abdevt/ndata
Page 731 and 732: Chapter 16. Integration of Ordinary
Page 733 and 734: 16.0 Introduction 709 problem where
Page 735 and 736: y(x) 16.1 Runge-Kutta Method 711 1
Page 737 and 738: } 16.1 Runge-Kutta Method 713 yt=ve
Page 739 and 740: 16.2 Adaptive Stepsize Control for
Page 747 and 748: 16.3 Modified Midpoint Method 723 H
Page 749 and 750: 16.4 Richardson Extrapolation and t
Page 751 and 752: 16.4 Richardson Extrapolation and t
Page 753: 16.4 Richardson Extrapolation and t
Page 757 and 758: 16.5 Second-Order Conservative Equa
Page 759 and 760: y 16.6 Stiff Sets of Equations 735
Page 761 and 762: 16.6 Stiff Sets of Equations 737 If
Page 763 and 764: 16.6 Stiff Sets of Equations 739 od
Page 765 and 766: } 16.6 Stiff Sets of Equations 741
Page 767 and 768: 16.6 Stiff Sets of Equations 743 Co
Page 769 and 770: 16.6 Stiff Sets of Equations 745 Se
Page 771 and 772: } 16.7 Multistep, Multivalue, and P
Page 773 and 774: 16.7 Multistep, Multivalue, and Pre
Page 775 and 776: 16.7 Multistep, Multivalue, and Pre
Page 777 and 778: Chapter 17. Two Point Boundary Valu
Page 779 and 780: equired boundary value 17.0 Introdu
Page 781 and 782: 17.1 The Shooting Method 17.1 The S
Page 783 and 784: } 17.1 The Shooting Method 759 floa
Page 785 and 786: 17.2 Shooting to a Fitting Point 76
Page 787 and 788: 17.3 Relaxation Methods 763 depende
Page 789 and 790: X X X X X X X X X X X X X X X X X X
Page 791 and 792: 17.3 Relaxation Methods 767 Next co
Page 793 and 794: 17.3 Relaxation Methods 769 calcula
Page 795 and 796: } 17.3 Relaxation Methods 771 for (
Page 797 and 798: 17.4 A Worked Example: Spheroidal H
Page 803 and 804: } 17.4 A Worked Example: Spheroidal
Page 805 and 806:
17.4 A Worked Example: Spheroidal H
Page 807 and 808:
17.5 Automated Allocation of Mesh P
Page 809 and 810:
17.6 Handling Internal Boundary Con
Page 811 and 812:
17.6 Handling Internal Boundary Con
Page 813 and 814:
18.0 Introduction 789 is called a F
Page 815 and 816:
18.1 Fredholm Equations of the Seco
Page 817 and 818:
#include "nrutil.h" 18.1 Fredholm E
Page 819 and 820:
18.2 Volterra Equations 795 in §18
Page 821 and 822:
18.3 Integral Equations with Singul
Page 823 and 824:
Page 825 and 826:
Page 827 and 828:
f (x) 1 .5 0 −.5 0 18.3 Integral
Page 829 and 830:
18.4 Inverse Problems and the Use o
Page 831 and 832:
18.4 Inverse Problems and the Use o
Page 833 and 834:
18.5 Linear Regularization Methods
Page 835 and 836:
Page 837 and 838:
Page 839 and 840:
18.6 Backus-Gilbert Method 815 nece
Page 841 and 842:
18.6 Backus-Gilbert Method 817 Subs
Page 843 and 844:
18.7 Maximum Entropy Image Restorat
Page 845 and 846:
Page 847 and 848:
Page 849 and 850:
Page 851 and 852:
Chapter 19. Partial Differential Eq
Page 853 and 854:
19.0 Introduction 829 possible stab
Page 855 and 856:
y L ∆ y1 19.0 Introduction 831 A
Page 857 and 858:
19.0 Introduction 833 So-called rap
Page 859 and 860:
19.1 Flux-Conservative Initial Valu
Page 861 and 862:
Page 863 and 864:
Page 865 and 866:
Page 867 and 868:
Page 869 and 870:
t or n 19.1 Flux-Conservative Initi
Page 871 and 872:
19.2 Diffusive Initial Value Proble
Page 873 and 874:
19.2 Diffusive Initial Value Proble
Page 875 and 876:
and the heuristic stability criteri
Page 877 and 878:
19.3 Initial Value Problems in Mult
Page 879 and 880:
19.3 Initial Value Problems in Mult
Page 881 and 882:
19.4 Fourier and Cyclic Reduction M
Page 883 and 884:
Page 885 and 886:
Page 887 and 888:
FACR Method 19.5 Relaxation Methods
Page 889 and 890:
19.5 Relaxation Methods for Boundar
Page 891 and 892:
Page 893 and 894:
Page 895 and 896:
19.6 Multigrid Methods for Boundary
Page 897 and 898:
Page 899 and 900:
S S S E γ = 1 19.6 Multigrid Metho
Page 901 and 902:
Page 903 and 904:
Page 905 and 906:
} 19.6 Multigrid Methods for Bounda
Page 907 and 908:
Page 909 and 910:
Page 911 and 912:
#include 19.6 Multigrid Methods fo
Page 913 and 914:
Chapter 20. Less-Numerical Algorith
Page 915 and 916:
20.1 Diagnosing Machine Parameters
Page 917 and 918:
20.1 Diagnosing Machine Parameters
Page 919 and 920:
(a) G(i) (b) MSB 4 3 2 1 0 LSB i MS
Page 921 and 922:
20.3 Cyclic Redundancy and Other Ch
Page 923 and 924:
Page 925 and 926:
Page 927 and 928:
} 20.4 Huffman Coding and Compressi
Page 929 and 930:
20.4 Huffman Coding and Compression
Page 931 and 932:
} 20.4 Huffman Coding and Compressi
Page 933 and 934:
} } } 20.4 Huffman Coding and Compr
Page 935 and 936:
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Page 937 and 938:
20.5 Arithmetic Coding 913 Individu
Page 939 and 940:
20.6 Arithmetic at Arbitrary Precis
Page 941 and 942:
} for (j=n;j>=1;j--) { ireg=u[j]+HI
Page 943 and 944:
#include "nrutil.h" #define RX 256.
Page 945 and 946:
} 20.6 Arithmetic at Arbitrary Prec
Page 947 and 948:
Page 949:
show all

Numerical recipes

Create successful ePaper yourself

Delete template?

Save as template?