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Knuth D.E. — The art of computer programming (Vol. 2. Seminumerical algorithms)
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Íàçâàíèå: The art of computer programming (Vol. 2. Seminumerical algorithms)Àâòîð: Knuth D.E. Àííîòàöèÿ: This multivolume work on the analysis of algorithms has long been recognized as the definitive description of classical computer science. The three complete volumes published to date already comprise a unique and invaluable resource in programming theory and practice. Countless readers have spoken about the profound personal influence of Knuth's writings. Scientists have marveled at the beauty and elegance of his analysis, while practicing programmers have successfully applied his "cookbook" solutions to their day-to-day problems. All have admired Knuth for the breadth, clarity, accuracy, and good humor found in his books. To begin the fourth and later volumes of the set, and to update parts of the existing three, Knuth has created a series of small books called fascicles, which will be published at regular intervals. Each fascicle will encompass a section or more of wholly new or revised material. Ultimately, the content of these fascicles will be rolled up into the comprehensive, final versions of each volume, and the enormous undertaking that began in 1962 will be complete. Volume 4, Fascicle 2 - This fascicle inaugurates the eagerly awaited publication of Knuth's "The Art of Co
ßçûê: Ðóáðèêà: Computer science /Àëãîðèòìû /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Èçäàíèå: 2nd editionÃîä èçäàíèÿ: 1981Êîëè÷åñòâî ñòðàíèö: 688Äîáàâëåíà â êàòàëîã: 18.11.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Percentage point 41 43 48 69—70 368 Perfect numbers 389 Perfect square 372 Period in a sequence 7—9 Period in a sequence, length of 4 7—8 15—22 34—36 392—393 Periodic continued fraction 359 398 Permanent 480 497 Permutation test 64 75 76 147 Permutation, encoding 64 75 139 Permutation, random 139—141 369 441 632 Perron, Oskar 339 Persian mathematics 181—182 265 309 443 Pervushin, Rev. Ivan Mikheevich 391 Peters, Johann (= Jean) Theodor 661 Pfeiffer, John Edward 176 Phalen, Harold Romaine 184 Phi 342 343 496 659—660 Phi 193 Phillips, Ernest William 185 Pi 38 144—145 152 154 182 184 193 268 342 659—660 Pingala Acharya 441 Pippenger, Nicholas John 639 Places 250 Planck, Max Karl Ernst Ludwig, constant 198 211 223 225—226 Plass, Michael Frederick 614 Playwriting 174—176 Pocklington, Henry Cabourn 397 Pointer machine 295 301 Poisson, Simeon Denis, distribution 53 132—133 135—136 517 Poker test 62 72 151 Polar coordinates 54 57 118 Polar method 117—118 120 130—131 Pollard, John Michael 369 385 396 608 652 Polynomial 399—401 Polynomial chains 475—479 499—501 Polynomial, addition 399—401 Polynomial, arithmetic modulo m 34—35 400—401 444 Polynomial, characteristic 480 Polynomial, content of 405—406 Polynomial, degree of 399 401 410 Polynomial, derivative of 421 470 631 Polynomial, discriminant of 619 628 632 Polynomial, division 401—420 468—469 515 Polynomial, evaluation 466—505 588 Polynomial, factorization 420—441 Polynomial, greatest common divisor 405—420 434—436 440 Polynomial, interpolation 281—282 484—486 490 492 498 641 Polynomial, irreducible 403 417 421 437—441 Polynomial, leading coefficient of 399 433 435 Polynomial, monic 399 401 402 405 436 500 Polynomial, multiplication 399—400 489—494 503 652 Polynomial, multivariate 399—400 403 418—419 436 438—439 479—505 Polynomial, over a field 401—403 405 417 420—431 436—441 Polynomial, over a unique factorization domain 403—420 431—441 Polynomial, primitive 404 417 Polynomial, primitive modulo p 28—29 404 Polynomial, primitive part 404—406 Polynomial, random 417 430 436—437 439 441 Polynomial, remainder sequence 408—418 420 435—436 657 Polynomial, resultant 415 619 Polynomial, roots 22 416 418 420 464 474—475 499 Polynomial, squarefree 421 436 440 Polynomial, string 418—419 Polynomial, subtraction 399—401 Pope, David Alexander 263 Popper, Karl Raimund 166 Portable random number generator 171—173 Porter, J. W. 356—357 Positional representation of numbers 144—145 159—160 164 179—197 302—312 Positive definite quadratic form 94 111 Positive semidefinite matrix 551 Potency 22—25 50 71 76 78 88 Power series see “Generating function” Power series, manipulation of 506—515 Power tree 444—445 462—463 Power, raising to a see “Exponentiation” Power, raising to a, factorial 281—282 497 597 664 Powers, Don M. 296 Powers, evaluation of 441—466 Powers, Raymond E. 380 391 PR 143 145 162 166—169 242 249 453 Pratt, Vaughan Ronald 339 395 441 Precision, double 230—237 263—264 278—279 Precision, quadruple 237 Precision, single: fitting in one computer word 199 Precision, unlimited 265 268 314 Preconditioning see “Adaptation” Primality tests 364 374—380 391—398 Prime element in a unique factorization domain 403 Prime number 316—317 353 364 615 Prime number, distribution 366—369 395—396 615 632—633 Prime number, factorization into 12—13 317 353 364—398 464 Prime number, large 14 276 374—378 388—394 397 432 480 Prime number, Mersenne 391—395 397 Prime number, theorem 366 615 Prime number, useful 276 390 391 614 652 Prime number, verifying primality 364 374—380 391—398 Primitive element modulo m 19—22 Primitive notations for numbers 179 182 Primitive part 404—406 Primitive part of a polynomial 404—406 Primitive polynomial 404 417 Primitive polynomial modulo p 28—29 404 Primitive recursive function 159 Primitive root 437 438 Probabilistic algorithms 2 379—380 385—386 396—397 428—430 439 630 Probability, over the integers 143 145 162 166—169 242 249 453 Probability: ratio of occurrence 142 165 Probert, Robert Lome 641 Programming languages 206 Pronouncing hexadecimal numbers 185 Proof of algorithms 265 266 319—320 Proofs, constructive versus nonconstructive 270 273—274 585 Proper factor see “Divisor” Proth, F. (or E.) 614 Pseudo-division of polynomials 407 416 Pseudo-random sequence 3 Ptolemaeus (= Ptolemy), Claudius 181 Public key cryptography 388—389 Purdom, Paul Walton, Jr. 519 Quadratic congruential sequence 25—26 34 Quadratic forms 94 385 503 Quadratic forms, minimizing, over the integers 94—98 105 111—112 Quadratic irrationality 342 359 380—382 398 Quadratic reciprocity law 377 394 396 614 Quadratic residues 397 638 Quadruple-precision arithmetic 237 Quandalle, Philippe 651 Quasi-random numbers 3 173 Quater-imaginary number system 189 193—194 268 Quaternary number system 179 183 Quick, Jonathan Horatio 74 Quinary number system 179 183 197 Quotient, of polynomials 402—404 407 416 Quotient: [u/v] 250—251 see Quotientpartial 83 342 345—353 615—616 Quotienttrial 255—260 263—264 266—267 Rabin, Michael Oser 380 389 396 397 430 Rabinowitz, Philip 264 Rademacher, Hans 86 Radioactive decay 6 128 132 Radix conversion 184 188 189 191 193—194 250 302—312 467 470 Radix conversion, floating point 309—312 Radix conversion, multiple-precision 309 311 Radix point 9 179 182 187—188 192—193 198 302 Radix, complex 189—190 193—194 268 Radix, irrational 193 Radix, mixed 64 99—100 183 192—196 266 274—275 309—310 486 Radix, negative 188—189 193—194 196 311 Radix: base of positional notation 179 Rail, Louis Baker 225 Raimi, Ralph Alexis 242 247 Raleigh, Sir Walter 183 Ramage, John Gerow 130 Ramanujan, SrTnivasa Aiyahgar 613 Ramaswami, Vammi 367 Ramshaw, Lyle Harold 157 Rand Corporation 2—3 Randell, Brian 186 209 Random bit 11 29—31 35—36 45 114—115 133 Random combination 136—141 Random direction 130—131 Random function 4—8 369 Random integer, among all positive integers 143 242 249 439 453 Random integer, in a bounded set 114—115 171 Random mapping 4—8 369 Random numbers 1—177 Random numbers, generating nonuniform deviates 114—136 Random numbers, generating uniform deviates 9—37 170—173 Random numbers, machines for generating 2—3 387 Random numbers, quasi- 3 173 Random numbers, summary 170—173 Random numbers, tables 2—3 152 Random numbers, testing 38—113 see Random numbers, using 1—2 114—141 615 see Random permutation 139—141 369 441 632 Random point, in a circle 117—118 Random point, in a sphere 131 Random point, on a sphere 130—131 Random point, on an ellipsoid 136 Random polynomial 417 430 436—437 439 441 Random random-number generator 4—8 25 Random sample 136—141 Random sequence, finite 145 161—164 Random sequence, meaning of 2 142—169 Random waiting time 114 Randomness, definitions of 142—169 Randomness, improving 25 31—34 37 RANDU 25 104 173 525 Range arithmetic 212 225—227 230 570 Rank, of a matrix 425—427 488 496 502 625 Rank, of a tensor 488—489 494—496 501—505 Rank, of apparition 393 Rapoport, Anatol 519 Ratio method 125—128 135 Rational arithmetic 68 313—316 409 506—507 Rational functions 401 479 500 Rational functions, approximation and interpolation 420 515 Rational number 313 401 439 Rational number, approximation 314—316 363—364 Rational number, positional representation 195 311 359 Real numbers 401 Real Time 270 Realization of a tensor 489 Reciprocal 264 295—297 403 Reciprocal differences 487 Reciprocal, floating point 228 Reciprocal, mod m 25 427 437 595 599 Reciprocity laws 79 86 377 394 396 614 Recorde, Robert, xi 265 Rectangle-wedge-tail method 118—123 134 Rectangular distribution see “Uniform distribution” Recurrence relations 9 25—29 33—37 246—247 279 280 285—286 288 295 296—297 300 332—333 392—395 481—482 506 507 519 568 597 630 637 654 655 recursive method 237 279 283—285 287 295 400 481—482 632 652—653 658 Reeds, James Alexander, III 561 Rees, David 36 163 Regular continued fraction 330 341—342 352—353 358—363 Reiser, John Fredrick, vii 28 36 227 Reitwiesner, George Walter 265 Rejection method 120—123 129 134—135 553 Relative error 206 213 216—217 237 240 Relatively prime 11 313 324 404 417 Remainder 250—251 256 402 407 416 515 see Replicative law 86 Representation of numbers see “Number system” Representation of oo 209 230 315 593 Representation of trees 463 530 555 634 Reservoir sampling 138—140 Residue arithmetic 269 see result set 475—476 499 Resultant of polynomials 415 619 Revah, Ludmila 647 Reverse of a polynomial 416 434 436 618 657 Reversing binary number system 196 Reversion of power series 508—511 514 Revolving binary number system 196 Rezucha, Ivan 137 Rhind papyrus 443 Rho method see “Monte Carlo method for factoring” Rieger, Georg Johann 605 Riemann, Georg Friedrich Bernhard 78 396 Riemann, hypothesis 366—367 380 632 Riemann, integration 146—147 244 Ring with identity, commutative 399 401 407 Riordan, John 520 Rivest, Ronald Linn 386 648 Robber 174—176 Robinson, Donald Wilford 528 Robinson, Julia Bowman 616 Robinson, Raphael Mitchel 614 652 Roman numerals 179 193 679 Romani, Francesco 482 Roof, Raymond Bradley 110 Roots of a polynomial 22 416 418 420 464 474—475 499 Roots of unity see “Cyclotomic polynomials” “Exponential Ross, Douglas Taylor 176 Rotenberg, Aubey 10 45 Roulette 9 53 240 Rounding 201 203 206 207 212 215—216 219 221—222 226 314—316 363—364 Rounding overflow 201 203 204 207 208 211—212 Rozier, Charles P. 308 RSA box 386—389 397 Rudolff, Christof 182 Rumely, Robert Scott 380 Run test 61 65—68 72 74 88 151 167 Runge, Carl David Tolme 642 Runs above (or below) the mean 61 Russian peasant method 443 Ruzsa, Imre Zoltan 197 Ryser, Herbert John 497 641 Sachau, Karl Eduard 441 Sahni, Sartaj 58 Saidan, Ahmad Salim 182 441 Salamin, Eugene 268 Samelson, Klaus 226—227 310 Samet, Paul Alexander 304 Sampling (without replacement) 1 136—141 Sampling weighted 141 Sands, Arthur David 567 Savage, John Edmund 648 Sawtooth function 77 86 Saxe, James Benjamin 136 Scarborough, James Blaine 226 Schmid, Larry Philip 71 Schmidt, Erhard, orthogonalization process 97 620 Schmidt, Wolfgang M. 169 Schnorr, Claus-Peter 166 397 478 Scholz, Arnold 459 Schonhage, Arnold 276 287—288 290 295 300 301 311 451 465 482 592 598 638 655 Schreyer, Helmut 186 Schroder, Ernst 512 Schroder, Ernst, function 512—513 Schroeppel, Richard Crabtree 383 384 Schwartz, Jacob Theodore 619 Schwarz, Stefan 430 Secrest, Don 265 310 secret keys 177 386—389 397 486 secure communications 386—389 397 Sedecimal number system 186 see Sedgewick, Robert 518
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