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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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342 360 611 629 659—660 666 209 230 315 593 144—155 164—168. 342 343 496 659—660 38 144—145 152 154 182 184 193 268 342 659—660 vii 689 0FL0 202 10-adic numbers 587 2-adic numbers 197 A priori tests 75 abacus 180 184 Abramowitz, Milton 41 611 Absolute error 293—294 Absorption laws 636 ACC: Floating point accumulator 202—203 232—233 Acceptance-rejection method 120—123 129 134—135 553 Accuracy of floating point arithmetic 206 213—230 237 311—312 420 466—467 Accuracy of random number generation 26 90—92 103 171 Adaptation of coefficients 471—479 498—501 Addition 178 191 194 197 250—252 262—263 265—268 Addition chains 444—466 501 Addition chains, 459—460 464 Addition chains, ascending 447 Addition chains, dual 462 466 Addition chains, star 447 453—457 461 463 Addition, complex 468 Addition, continued fractions 602 Addition, floating point 199—204 209 211—216 219—230 232—234 237 238—239 249 Addition, fractions 313—315 Addition, mixed-radix 193 266 589 Addition, mod m 11 14—15 171 187 271—272 Addition, modular 269 277 Addition, multiple-precision 250—252 262—263 265—268 Addition, polynomial 399—401 Addition, power series 506 Addition-subtraction chains 465 Additive random number generation 26—30 36—37 171—173 Adleman, Leonard Max 380 386 396 Admissible numbers 165 Ahrens, Joachim Heinrich Ludecke 114 124 125 128 129 131 132 133 135 136 553 Ahrens, Wilhelm Ernst Martin Georg 192 al-Biruni, abu Rayhan Muhammad ibn Ahmad 441 al-Kasht, Jemshid ibn Mes'ud 182 309 443 al-Khwarizmi, abu Ja'far Muhammad ibn Miisa 181 265 al-Uqlidisi, abu al-Hasan, Ahmad ibn Ibrahim 182 265 441 Alanen, Jack David 29 Alekseev, Boris Vasil'evich 112 Algebra, free associative 418—419 Algebraic dependence 499 Algebraic integers 380 Algebraic number field 314 316 632—633 Algol 265 Algorithms, analysis of 7—8 73—74 135 140 238—249 262—263 266—267 278—280 285—289 293—297 300—301 311 330—364 367—369 383—386 397—398 417 420 427—429 436—441 451 481—482 497 503—505 511 513—514 654 Algorithms, complexity of 133 265 299 301 444—466 475—479 487—505 Algorithms, historical development of 318—320 441 443 Algorithms, proof of 265 266 319—320 Alias method 115—116 122 134 555 Alt, Helmut 647 Analysis of Algorithms 7—8 73—74 135 140 238—249 262—263 266—267 278—280 285—289 293—297 300—301 311 330—364 367—369 383—386 397—398 417 420 427—429 436—441 451 481—482 497 503—505 511 513—514 654 Analytical engine 185 Ananthanarayanan, Kasi 123 AND (logical and) 305 312 373—374 434 617 Anderson, Stanley F. 296 Anderson, Theodore Wilbur 71 Antanairesis 318—319 362 Apollonius of Perga 209 Apparition, rank of 393 Approximate equality 208 217—219 228—229 Approximately linear density 120—121 Approximation, by rational functions 420 515 Approximation, by rational numbers 314—316 363—364 Arabic mathematics 181—182 265 309 441 443 Arbitrary precision 265 268 314 Archibald, Raymond Clare 185 Arctangent 297 Arithmetic 178—515 see “Comparison” “Division” “Doubling” “Exponentiation” “Greatest “Halving” “Multiplication” “Reciprocal” “Square “Subtraction” Arithmetic chains 646 Arithmetic, complex 189—190 212 268 292—294 467—468 482 487 497 501 641—642 647 Arithmetic, floating point 198—249 443 Arithmetic, fractions 68 313—316 409 506—507 Arithmetic, fundamental theorem of 317 364 464 Arithmetic, mod m 11—15 171—172 187 271—272 277 443 Arithmetic, modular 268—278 287—290 431—441 486 Arithmetic, multiple-precision 250—301 327—330 339 Arithmetic, polynomial 399—505 Arithmetic, power series 506—515 Arithmetic, rational 68 313—316 409 506—507 Arrival time 128 Ashenhurst, Robert Lovett 225 227 310 Aspvall, Bengt Ingemar vii Associative law 214 217 224—225 227 229 399 636 Asymptotic values: functions that express the limiting behavior approached by numerical quantities 57 248 398 451—453 506 520 Atanasoff, John Vincent 186 Atrubin, Allan Joseph 299 Aurifeuille, Leon Francois Antoine 376 Automata (plural of Automaton) 295 297—301 311 398 Automorphic numbers 278 Avogadro, Amedeo, number 198 211 223 225—226 Axioms for floating point arithmetic 214—218 227—229 b-ary number 144 b-ary sequence 144—146 164 Babbage, Charles 185 Babenko, Konstantin Ivanovich 350 361 Babington — Smith, Bernard 2—3 72—73 Babylonian mathematics 180 209 318 Bachet, Claude Gaspard, sieur de Meziriac 192 Bachmann, Paul Gustav Heinrich 605 Bag 636 Baker, Kirby Alan 300 Balanced decimal number system 195 Balanced mixed-radix number system 100 586 Balanced ternary number system 190—193 211 268 336 Ballantine, John Perry 263 Bareiss, Erwin Hans 276 416 Barton, David Elliott 72 Base of representation 179 Base of representation, floating point 198 210—211 248 Bauer, Friedrich Ludwig 226—227 310 Baumgart, Bruce Guenther 90 Bays, John Carter 32 Beckenbach, Edwin Ford 130 Becker, Oskar Joachim 342 Belaga, Eduard Grigor'evich 477 Bell Telephone Laboratories Model V 209 Bellman, Richard Ernest ix Benford, Frank 240 Bentley, Jon Louis 136 Berglund, Glenn David 642 Bergman, George Mark 620 Berlekamp, Elwyn Ralph vi 420 423 429 436 625 Bernoulli, James (= Jakob = Jacques) 184 Bernoulli, numbers 661 Bernoulli, sequences 165 Besicovitch, Abram Samoilovitch 165 Beta distribution 129—131 Beyer, William Aaron 110 Bharati Krishna Tirtharji Maharaja, Jagadguru Swami Sri, shankaracharya of Goverdhana Matha 192 Bienayme, Irenee Jules 72 Bilinear forms 487—496 502—505 Billingsley, Patrick Paul 611 Bin-packing problem 550 Binary basis 196 Binary computer: A computer that manipulates numbers primarily in the binary (radix 2) number system 29—31 186 311 322 373—374 617 Binary digit 179 184 Binary gcd algorithms 321—323 330—339 417 Binary method for exponentiation 441—444 463—465 Binary number systems 179 182—190 193—197 400 441 464 Binary point 179 Binary search 307 Binary trees 639 Binary-coded decimal 186 305 311—312 Binary-decimal conversion 302—312 Binet, Jacques Phillipe Marie 605 Bini, Dario 482 654—655 Binomial distribution 131—133 136 385 531 Binomial distribution, continuous 553 Binomial distribution, negative 135 Binomial distribution, tail 160 Binomial number system 193 Binomial theorem 507 Birnbaum, Zygmunt Wilhelm 55 bit manipulation see “Boolean operations” Bit, random 11 29—31 35—36 45 114—115 133 Bit: "Binary digit," either zero or unity 179 184 Bjoerk, Johan Harry 229 Bluestein, Leo I. 588 Blum, Bruce Ivan 265 Blum, Fred 415 499 Bofinger, Eve 535 Bofinger, Victor John 535 Bohlender, Gerd 573 Boolean operations 29—31 177 186 305 311—312 322 373—374 434 439 617 629 637 Border rank 505 Borel, Emile Felix Edouard Justin 164 Borodin, Allan Bertram 479 486 496 648 Borosh, Itzhak 104 113 276 548 Borrow 252 258 266 Bouyer, Martine 268 Bowden, Joseph 185 Box, George Edward Pelham 117 Boyer, Carl Benjamin 182 Bradley, Gordon Hoover 325 362 Bramhall, Janet Natalie 511 Brauer, Alfred Theodor 451 459 464 Bray, Thomas Arthur 123 521 Brent, Richard Peirce, vii 7 27 125 131 134 136 226 265 297 335 338 339 367 371 482 510 512—513 515 530 584 597 608 656 657 Bright, Herbert Samuel 30 Brillhart, John David, vi 28 378 380 384 Brockett, Roger Ware 652 Brooks, Frederick Phillips 210 Brouwer, Luitzen Egbertus Jan 166 Brown, D. J. Spencer 637 Brown, George William 130 Brown, Mark Robbin 652 Brown, William Stanley 401 410 420 435 629 Brute force 596 Buchholz, Werner 186 210 Buckholtz, Thomas Joel 661 Bunch, James Raymond 482 Buneman, Oscar 647 Burks, Arthur Walter 186 Cahen, Eugene 621 Calculating prodigies 279 Campbell, Sullivan Graham 210 Cancellation error 230 Cancellation error, avoiding 574 Cantor, David Geoffrey 430—431 Cantor, Georg Ferdinand Louis Philippe 193 Capovani, Milvio 482 Caramuel Lobkowitz, Juan 183 Cards, playing 139 174 Carlitz, Leonard 79 86 Carmichael, Robert Daniel 19 Carmichael, Robert Daniel, numbers 609 613 Carr, John Weber, III 210 226 227 Carry 189 191 232—234 250—254 258 261—263 265—266 400 450 456 Cassels, John William Scott 105 151 Casting out nines 273 287 307 Catalan, Eugene Charles, numbers 639 Cauchy, Augustin Louis 192 314 506 Cauchy, inequality: 95 216 CDC 1604 276 Ceiling function 77 665 Cesaro, Ernesto 337 Chain step 475 500—503 Chaitin, Gregory John 164 166 Chan, Tony Fan-Cheong 572 Chappie, M. A. 511 CHAR (convert to characters) 311 Characteristic 199 see Characteristic polynomial 480 Charles XII of Sweden 184 Chartres, Bruce Aylwin 227 Chebotarev, Nikolai Grigor'evich 632 Cheng, Russell Ch'uan Hsun 130 Chhin Chiu Shao 271 Chi-square distribution 41 45 47 65 130 Chi-square table 41 Chi-square test 39—45 50—54 56—59 Chinese mathematics 181—182 271 Chinese remainder algorithm 20 274 277 289 435—436 486 Chinese remainder theorem 269—271 373 629 Chinese remainder theorem, for polynomials 437 (exercise 3) 486 490—492 Chinese remainder theorem, generalized 276 Chirp transform 588 (exercise 8) Choice, random 2 114—116 122 134 Christiansen, Hanne Delgas 72 Church, Alonzo 165 Classical algorithms 250—268 Cochran, William Gemmell 53 Cocke, John 212 Coefficients of a polynomial 399 Coefficients of a polynomial, adaptation of 471—479 498—501 Coefficients of a polynomial, Cohen, Daniel Isaac Aryeh 579 Coefficients of a polynomial, size of 401 414 432—433 438—439 Cohn, Paul Moritz 418 620 Colenne, Joseph Desire 185 Collins, George Edwin, vi 264 265 357 401 410 434 435 441 595 622 Collision test 68—70 72—73 151 Colson, John 192 Colton, Rev. Charles Caleb vii Combination of random number generators 31—33 36—37 Combination, random 136—141 Combinations with repetitions 614 Combinatorial matrix 112 Common divisors 419 see Commutative law 214 316 636 639 Commutative ring with identity 399 401 407 Companion matrix 494 Comparison, continued fractions 606 Comparison, floating point 208 217—219 224 227—229 Comparison, fractions 315 Comparison, mixed-radix 274—275 Comparison, modular 274—275 Comparison, multiple-precision 266 Complement notations for numbers 14—15 186—187 194 197 212 261 262 264 272 Complete binary tree 555 Completely equidistributed sequence 164 Complex arithmetic 189—190 212 268 292—294 467—468 482 487 497 501 641—642 647 Complex number representation 189—190 193—194 196 268 401 Complexity of calculation 133 265 299 301 444—466 475—479 487—505 Composition of power series 514 656 Computability 154—156 164—166 169 Computational complexity 133 265 299 301 444—466 475—479 487—505 Congruential sequence, linear 9—11 Congruential sequence, linear, choice of increment 10 15 21 84—85 93 171 Congruential sequence, linear, choice of modulus 11—15 170 Congruential sequence, linear, choice of multiplier 10 15—25 84—86 98—105 170—171 Congruential sequence, linear, choice of seed 15 19 137 170 Congruential sequence, linear, period length 15—22 Congruential sequence, linear, subsequence of 10 71 Congruential sequence, quadratic 25—26 34 Conjugate of complex number 642 667 Content of a polynomial 405—406 Context-free grammar 636 Continuant polynomials 340—343 358 361—363 420 548 604 605 607 621 Continued fractions 339—340 479 500 Continued fractions, infinite 341 358 Continued fractions, quadratic irrationality 342 359 380—382 398 Continued fractions, regular 330 341—342 352—353 358—363
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