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Knuth D.E. — The art of computer programming (vol. 2 Seminumerical Algorithms)
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:

Volume 2 of Donald Knuth's classic series The Art of Computer Programming covers seminumerical algorithms, with topics ranging from random number generators to floating point operations and other optimized arithmetic algorithms. Truly comprehensive and meticulously written, this book (and series) is that rarest of all creatures — a work of authoritative scholarship in classical computer science, but one that can be read and used profitably by virtually all working programmers.
The book begins with fundamental questions regarding random numbers and how to use algorithms to generate them. Subsequent chapters demonstrate efficient computation of single-precision and double-precision arithmetic calculations and modular arithmetic. The text then presents prime factorization (which can be used in cryptography, for instance) and algorithms for calculating fractions. This volume ends with algorithms for polynomial arithmetic and manipulation of power-series topics, which will benefit those with some knowledge of calculus.

Throughout this beautifully presented edition, Knuth incorporates hundreds of useful exercises for trying out the algorithms. These range from simple problems to larger research project topics. (The book provides answers, where appropriate, at the end of the book.) The result is a text that's suitable for college or graduate-level computer science courses or individual study by programmers. Volume 2 is an indispensable part of any working programmer's library.


ßçûê: en

Ðóáðèêà: Computer science/Àëãîðèòìû/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: third edition

Ãîä èçäàíèÿ: 1997

Êîëè÷åñòâî ñòðàíèö: 762

Äîáàâëåíà â êàòàëîã: 18.11.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$l^0$-chain      479 483 485
$L^3$ algorithm      118 417 453
$\$$_{N}$      170
$\chi^2$      42 56
$\gamma$ (Euler's constant)      359 379 726—727 733
$\infty$, representation of      225 244—245 332
$\infty$-distributed sequence      151—161 177 180—182
$\phi$ (golden ratio)      164 283 359 360 514 652 726—727 733
$\phi$ (golden ratio), logarithm of      283
$\phi$ (golden ratio), number system      209
$\pi$ (circle ratio)      41 151 158 161 198 200 279—280 284 358 726—727 733
$\pi(x)$ (prime count)      381—382 416
$\TeX$      iv vi 762
$\varphi(n)$ (totient function)      19—20 289 369 376 583 646
0-origin indexing      444 512
10-adic numbers      632
1009      vi 188 413 661
2-adic numbers      213
69069      75 106 108
A priori tests      80
abacus      196
Abacus, binary      200
Abel, Niels Henrik, binomial theorem      58 535
Abramowitz, Milton      44
Absolute error      240 309 312—313
Absorption laws      694
Abuse of probability      433
Abuse of theory      88
ACC: Floating point accumulator      218—219 248—249
Acceptance-rejection method      125—126 128—129 134 138 139 591
Accuracy of floating point arithmetic      222 229—245 253 329 438 485
Accuracy of random number generation      27 95 105 185
adaptation of      490—494 516—517
Adaptation of coefficients      490—494 516—517
Add-with-carry sequence      23 35 72 108 547
Addition      194 207 210 213 265—267
Addition chains      465—485 494 519
Addition chains, $l^{0}-$      479 483 485
Addition chains, ascending      467
Addition chains, dual      481 485
Addition chains, star      473—477 480 482 467
Addition, complex      487
Addition, continued fractions      649
Addition, double-precision      247—249 251
Addition, floating point      215—220 227—228 230—231 235—238 253—254 602
Addition, fractions      330—331
Addition, left to right      281
Addition, mixed-radix      281
Addition, mod m      12 15 203 287—288
Addition, modular      285—286 293
Addition, multiprecision      266—267 276—278 281 283
Addition, polynomial      418—420
Addition, power series      525
Addition, sideways      463
Addition-subtraction chains      484
Additive random number generation      27—29 39—40 186—188 193
Adleman, Leonard Max      396 403 405 414 417 671
Admissible numbers      177
Ahrens, Joachim Heinrich Ludecke      119 129—130 133 134 136 137 140 141 588
Ahrens, Wilhelm Ernst Martin Georg      208
Akushsky, Izrail Yakovlevich (Àêóøñêèé, Èçðàèëü ßêîâëåâè÷)      292
al-Biruni, Abu al-Rayhan Muhammad ibn Ahmad      461
al-Kashi, Jamshid ibn Mas'ud      198 326 462
al-Khwarizmi, Abu 'Abd Allah Muhammad ibn Musa      197 280
al-Samaw'al (= as-Samaw'al), ibn Yahya ibn Yahuda al-Maghribi      198
al-Uqlidisi, Abu al-Hasan Ahmad ibn Ibrahim      198 280—281 461
Ala-Nissila, Tapio      75 570
Alanen, Jack David      30
Aldous, David John      145
Alekseev, Boris Vasilievich (Àëåêñååâ, Áîðèñ Âàñèëüåâè÷)      117
Alekseyev, Valery Borisovich (Àëåêñååâ, Âàëåðèé Áîðèñîâè÷)      699
Alexi, Werner      669
Alford, William Robert      659
Algebra, free associative      437
Algebraic dependence      496 518
Algebraic functions      533
Algebraic integers      396
Algebraic number fields      331 333 345 403 674
Algebraic system: A set of elements together with operations defined on them      see “Field” “Ring” “Unique
Algol      279
Algorithm      439—447
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, analysis of      7—9 76 140 147 276—278 281 301—302 348—356 360—373 377—378 382—384 399—400 435 445—447 455—456 530—532 658 714
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, complexity of      138 178—179 280 294—318 396 401—402 416 453 465—485 494—498 516—524 720
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, discovery of      99
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, historical development of      335 461—462
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, proof of      281—282 336—337 592
Alias method      120 127 139
Allouche, Jean-Paul      656
ALPAK      419
Alt, Franz Leopold      706
American National Standards Institute      226 246 600 602
Amplification of guesses      172—174 416—417
Analysis of Algorithms      7—9 76 140 147 276—278 281 301—302 348—356 360—373 377—378 382—384 399—400 435 445—447 455—456 530—532 658 714
Analysis of algorithms, history      360
Analytical engine      189 201
Ananthanarayanan, Kasi      128
AND (bitwise and)      140 188 322 328—329 389—390 453 671
Anderson, Stanley F.      312
ANSI: The American National Standards Institute      226 246 600 602
Antanairesis      335—336 378
Apollonius of Perga      225
Apparently random numbers      3—4 170—171
Apparition, rank of      410—411
Approximate associative law      232—233 239—240 244
Approximate equality      224 233—235 239 242—243 245
Approximately linear density      126
Approximation, by rational functions      438—439 534
Approximation, by rational numbers      331—332 378—379 617
Arabic mathematics      197 280—281 326 461—462
Arazi, Benjamin      396
Arbitrary precision      279 283 331 416
Arbogast, Louis Francois Antoine      722
Archibald, Raymond Clare      201
Arctangent      313 628
Aristotle of Stagira, son of Nicomachus      335
Arithmetic      194—537 (see “Addition” “Comparison” “Division” “Doubling” “Exponentiation” “Greatest “Halving” “Multiplication” “Reciprocal” “Square “Subtraction”)
Arithmetic chains      see “Quolynomial chains”
Arithmetic, complex      205 228 283 292 307—310 487 501 506 519 700 706
Arithmetic, floating point      214—264
Arithmetic, fractions      330—333 420 526
Arithmetic, fundamental theorem of      334 422 483
Arithmetic, mod m      12—16 185—186 203 284 287—288
Arithmetic, modular      284—294 302—305 450 454 499
Arithmetic, multiprecision      265—318
Arithmetic, polynomial      418—524
Arithmetic, power series      525—537
Arithmetic, rational      330—333 420 526
Armengaud, Joel      409
Arrival time      132
Arwin, Axel      687
Aryabhata      343
ASCII: The American Standard Code for Information Interchange      417
Ashenhurst, Robert Lovett      240 242 327
Associative law      229—233 242 341 418 694
Associative law, approximate      232—233 239—240 244
Asymptotic values: functions that express the limiting behavior approached by numerical quantities      59—60 79 263—264 355 372—373 377—378 415 472 525 541—542 659 686 722
Atanasoff, John Vincent      202
Atkin, Arthur Oliver Lonsdale      681
Atrubin, Allan Joseph      315
Automata (plural of Automaton)      313—317 329 416
Automorphic numbers      293—294
Avogadro di Quaregna e Cerreto, Lorenzo Romano Amedeo Carlo, number      214 227 238 240
Axioms for floating point arithmetic      230—231 242—245
b-ary number      151
b-ary sequence      151—153 177
Babbage, Charles      201
Babenko, Konstantin Ivanovich (Áàáåíêî, Êîíñòàíòèí Èâàíîâè÷)      366 376
Babington-Smith, Bernard      3 74 76
Babylonian mathematics      196 225 335
Bach, Carl Eric      396 661 663 689
Bachet, Claude Gaspard, sieur de Meziriac      208
Bag      694
Bailey, David Harold      284 634
Baker, Kirby Alan      316
Balanced binary number system      213
Balanced decimal number system      211
Balanced mixed—radix number system      103 293 631
Balanced ternary number system      207—208 209 227 283 353
Ballantine, John Perry      278
Bareiss, Erwin Hans      262 292 434
Barlow, Jesse Louis      262
Barnard, Robert      292
Barnsley, Michael Fielding      206
Barton, David Elliott      74 566
Barycentric coordinates      567
Base of representation      195
Base of representation, floating point      214—215 254 263
BASEBALL      378
Bauer, Friedrich Ludwig      241—242 327
Baum, Ulrich      701
Baur, Walter      718
Bays, John Carter      34
Beauzamy, Bernard      452 461 683 684
Beckenbach, Edwin Ford      135
Becker, Oskar Joachim      359
Bejian, Robert      164
Belaga, Edward Grigorievich (Áåëàãà, Ýäóàðä Ãðèãîðüåâè÷)      496
Bell Telephone Laboratories Model V      225
Bellman, Richard Ernest      ix.
Ben-Or, Michael      669
Benford, Frank      255
Bentley, Jon Louis      141
Bergman, George Mark      676
Berkowitz, Stuart J.      718
Berlekamp, Elwyn Ralph      439 449 456 681
Bernoulli, Jacques (= Jakob = James)      200
Bernoulli, numbers $B_n$      355 569
Bernoulli, numbers, table      728
Bernoulli, sequences      177
Bernstein, Daniel Julius      724
Besicovitch, Abram Samoilovitch (Áåçèêîâè÷, Àáðàì Ñàìîéëîâè÷)      178
Beta distribution      134—135
Beyer, William Aaron      115
Bharati Krishna Tirthaji Maharaja, Jagadguru Swami Sri, Shankaracharya of Goverdhana Matha      208
Bhaskara Acharya I      343
Bienayme, Irenee Jules      74
Bilinear forms      506—514 520—524
Billingsley, Patrick Paul      384 661
Bin-packing problem      585
Binary abacus      200
Binary basis      212
Binary computer: A computer that manipulates numbers primarily in the binary (radix 2) number system      30—32 201—202 276 328 339 389—390
Binary digit      195 200
Binary gcd algorithms      338—341 348—356 435
Binary gcd algorithms, compared to Euclid's      341
Binary gcd algorithms, extended      356
Binary method for exponentiation      461—463 466 482 696
Binary number systems      195 198—206 209—213 419 461 483
Binary point      195
Binary recurrences      318 634 714
Binary search      324
Binary shift      322 339 481 637 686
Binary trees      378 527 696 723
Binary-coded decimal      202 322 328—329
Binary-decimal conversion      319—329
BINEG      205
Binet, identity: $\Sigma^{n}_{j=1}a_{j}x_{j} \Sigma^{n}_{k=1}b_{k}y_{k} = \Sigma^{n}_{j=1}a_{j}y_{j} \Sigma^{n}_{k=1}b_{k}x_{k} + \Sigma_{1 \leq j < k \leq n} (a_{j}b_{k}-a_{k}b_{j})(x_{j}y_{k}-x_{k}y_{j})$      564
Binet, Jacques Philippe Marie      653
Bini, Dario Andrea      500 505 515 714 715 721
Binomial coefficients      416 516 622
Binomial distribution      136—138 141 401 559
Binomial distribution, tail of      167
Binomial number system      see “Combinatorial number system”
Binomial theorem      526 534
Birnbaum, Zygmunt Wilhelm      57
Birthday spacings      34 71—72 78—79 188
Bit: "Binary digit", either zero or unity      195 200
Bit: "Binary digit", random      12 30—32 35—36 38 48 119—120 170—176
Bitwise operations      see “Boolean operations”
Bjork, Johan Harry      244
Blachman, Nelson Merle      205
Black Box      455
Bleichenbacher, Daniel      478
Blinn, James Frederick      630
Blote, Hendrik Willem Jan      29
Blouin, Francois Joseph Raymond Marcel      582
Bluestein, Leo Isaac      634
Blum, Bruce Ivan      279
Blum, Fred      433 518
Blum, integer      174 416
Blum, Lenore Carol      36 599
Blum, Manuel      36 174 179 599
Bofinger, Eve      563
Bofinger, Victor John      563
Bohlender, Gerd      242 616
Bojaniczyk, Adam Wojciech      646
Bombieri, Enrico      683
Bombieri, norm      458 684
Boolean operations      30—31 140 202 328—329 389—390 459 605
Boolean operations, and      140 188 322 328—329 389—390 453 671
Boolean operations, exclusive or      31 32 193 419
Boolean operations, or      140 686 695
Boolean operations, shifts      322 339 481 637 686
Border rank      522—523
Borel, Emile Felix Edouard Justin      177
Borodin, Allan Bertram      498 505 515 707
Borosh, Itzhak      106—107 117 291 584
Borrow: A negative carry      267 273 281 545
Borwein, Peter Benjamin      284
Bosma, Wiebren      665
Bouyer, Martine      280
Bowden, Joseph      201
Box, George Edward Pelham      122
Boyar, Joan      599
Boyd, David William      691
Bradley, Gordon Hoover      343 378
Brakke, Kenneth Allen      608
Bramhall, Janet Natalie      530
Brauer, Alfred Theodor      470 478 483 690
Bray, Thomas Arthur      33 128 544
Brent, Richard Peirce      8 28 40 130 136 139 141 241 279 280 313 348 352—353 355 356 382 386 403 501 529—534 539—540 556 590 600 643 644 646 657 695 719—721
Brezinski, Claude      357 721
Brillhart, John David      29 394 396 400 660
Brockett, Roger Ware      712
Brocot, Achille      655
Bronte, Emily Jane      292
Brooks, Frederick Phillips, Jr.      226
Brouwer, Luitzen Egbertus Jan      179
Brown, David      see “Spencer Brown”
Brown, George William      135
Brown, Mark Robbin      712
Brown, Robert      see “Brownian motion”
Brown, William Stanley      419 428 438 454 686
Brownian motion      559
Bruijn, cycle      38—40
Brute force      642
Bshouty, Nader Hanna      700
Buchholz, Werner      202 226
Bunch, James Raymond      500
Buneman, Oscar      706
Burgisser, Peter      515
Burks, Arthur Walter      202
Burrus, Charles Sidney      701
Butler, James Preston      77
Butler, Michael Charles Richard      442
C language      185—188 193 327 556
Cahen, Eugene      676
Calculating prodigies      279 295
Camion, Paul Frederic Roger      449
Campbell, Edward Fay, Jr.      vii.
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