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

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Ќазвание: The art of computer programming (vol. 2 Seminumerical Algorithms)

јвтор: Knuth D.E.

јннотаци€:

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 Ч 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.


язык: en

–убрика: Computer science/јлгоритмы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: third edition

√од издани€: 1997

 оличество страниц: 762

ƒобавлена в каталог: 18.11.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$l^0$-chain      479 483 485
$L^3$ algorithm      118 417 453
$\$$_{N}$      170
$\chi^2$      42 56
$\gamma$ (Euler's constant)      359 379 726Ч727 733
$\infty$, representation of      225 244Ч245 332
$\infty$-distributed sequence      151Ч161 177 180Ч182
$\phi$ (golden ratio)      164 283 359 360 514 652 726Ч727 733
$\phi$ (golden ratio), logarithm of      283
$\phi$ (golden ratio), number system      209
$\pi$ (circle ratio)      41 151 158 161 198 200 279Ч280 284 358 726Ч727 733
$\pi(x)$ (prime count)      381Ч382 416
$\TeX$      iv vi 762
$\varphi(n)$ (totient function)      19Ч20 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 312Ч313
Absorption laws      694
Abuse of probability      433
Abuse of theory      88
ACC: Floating point accumulator      218Ч219 248Ч249
Acceptance-rejection method      125Ч126 128Ч129 134 138 139 591
Accuracy of floating point arithmetic      222 229Ч245 253 329 438 485
Accuracy of random number generation      27 95 105 185
adaptation of      490Ч494 516Ч517
Adaptation of coefficients      490Ч494 516Ч517
Add-with-carry sequence      23 35 72 108 547
Addition      194 207 210 213 265Ч267
Addition chains      465Ч485 494 519
Addition chains, $l^{0}-$      479 483 485
Addition chains, ascending      467
Addition chains, dual      481 485
Addition chains, star      473Ч477 480 482 467
Addition, complex      487
Addition, continued fractions      649
Addition, double-precision      247Ч249 251
Addition, floating point      215Ч220 227Ч228 230Ч231 235Ч238 253Ч254 602
Addition, fractions      330Ч331
Addition, left to right      281
Addition, mixed-radix      281
Addition, mod m      12 15 203 287Ч288
Addition, modular      285Ч286 293
Addition, multiprecision      266Ч267 276Ч278 281 283
Addition, polynomial      418Ч420
Addition, power series      525
Addition, sideways      463
Addition-subtraction chains      484
Additive random number generation      27Ч29 39Ч40 186Ч188 193
Adleman, Leonard Max      396 403 405 414 417 671
Admissible numbers      177
Ahrens, Joachim Heinrich Ludecke      119 129Ч130 133 134 136 137 140 141 588
Ahrens, Wilhelm Ernst Martin Georg      208
Akushsky, Izrail Yakovlevich (јкушский, »зраиль яковлевич)      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 280Ч281 461
Ala-Nissila, Tapio      75 570
Alanen, Jack David      30
Aldous, David John      145
Alekseev, Boris Vasilievich (јлексеев, Ѕорис ¬асильевич)      117
Alekseyev, Valery Borisovich (јлексеев, ¬алерий Ѕорисович)      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 УFieldФ УRingФ УUnique
Algol      279
Algorithm      439Ч447
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, analysis of      7Ч9 76 140 147 276Ч278 281 301Ч302 348Ч356 360Ч373 377Ч378 382Ч384 399Ч400 435 445Ч447 455Ч456 530Ч532 658 714
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, complexity of      138 178Ч179 280 294Ч318 396 401Ч402 416 453 465Ч485 494Ч498 516Ч524 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 461Ч462
Algorithms: Precise rules for transforming specified inputs into specified outputs in a finite number of steps, proof of      281Ч282 336Ч337 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      172Ч174 416Ч417
Analysis of Algorithms      7Ч9 76 140 147 276Ч278 281 301Ч302 348Ч356 360Ч373 377Ч378 382Ч384 399Ч400 435 445Ч447 455Ч456 530Ч532 658 714
Analysis of algorithms, history      360
Analytical engine      189 201
Ananthanarayanan, Kasi      128
AND (bitwise and)      140 188 322 328Ч329 389Ч390 453 671
Anderson, Stanley F.      312
ANSI: The American National Standards Institute      226 246 600 602
Antanairesis      335Ч336 378
Apollonius of Perga      225
Apparently random numbers      3Ч4 170Ч171
Apparition, rank of      410Ч411
Approximate associative law      232Ч233 239Ч240 244
Approximate equality      224 233Ч235 239 242Ч243 245
Approximately linear density      126
Approximation, by rational functions      438Ч439 534
Approximation, by rational numbers      331Ч332 378Ч379 617
Arabic mathematics      197 280Ч281 326 461Ч462
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      194Ч537 (see УAdditionФ УComparisonФ УDivisionФ УDoublingФ УExponentiationФ УGreatest УHalvingФ УMultiplicationФ УReciprocalФ УSquare УSubtractionФ)
Arithmetic chains      see УQuolynomial chainsФ
Arithmetic, complex      205 228 283 292 307Ч310 487 501 506 519 700 706
Arithmetic, floating point      214Ч264
Arithmetic, fractions      330Ч333 420 526
Arithmetic, fundamental theorem of      334 422 483
Arithmetic, mod m      12Ч16 185Ч186 203 284 287Ч288
Arithmetic, modular      284Ч294 302Ч305 450 454 499
Arithmetic, multiprecision      265Ч318
Arithmetic, polynomial      418Ч524
Arithmetic, power series      525Ч537
Arithmetic, rational      330Ч333 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      229Ч233 242 341 418 694
Associative law, approximate      232Ч233 239Ч240 244
Asymptotic values: functions that express the limiting behavior approached by numerical quantities      59Ч60 79 263Ч264 355 372Ч373 377Ч378 415 472 525 541Ч542 659 686 722
Atanasoff, John Vincent      202
Atkin, Arthur Oliver Lonsdale      681
Atrubin, Allan Joseph      315
Automata (plural of Automaton)      313Ч317 329 416
Automorphic numbers      293Ч294
Avogadro di Quaregna e Cerreto, Lorenzo Romano Amedeo Carlo, number      214 227 238 240
Axioms for floating point arithmetic      230Ч231 242Ч245
b-ary number      151
b-ary sequence      151Ч153 177
Babbage, Charles      201
Babenko, Konstantin Ivanovich (Ѕабенко,  онстантин »ванович)      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 mixedЧradix number system      103 293 631
Balanced ternary number system      207Ч208 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      214Ч215 254 263
BASEBALL      378
Bauer, Friedrich Ludwig      241Ч242 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 (Ѕелага, Ёдуард √ригорьевич)      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 (Ѕезикович, јбрам —амойлович)      178
Beta distribution      134Ч135
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      506Ч514 520Ч524
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      30Ч32 201Ч202 276 328 339 389Ч390
Binary digit      195 200
Binary gcd algorithms      338Ч341 348Ч356 435
Binary gcd algorithms, compared to Euclid's      341
Binary gcd algorithms, extended      356
Binary method for exponentiation      461Ч463 466 482 696
Binary number systems      195 198Ч206 209Ч213 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 328Ч329
Binary-decimal conversion      319Ч329
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      136Ч138 141 401 559
Binomial distribution, tail of      167
Binomial number system      see УCombinatorial number systemФ
Binomial theorem      526 534
Birnbaum, Zygmunt Wilhelm      57
Birthday spacings      34 71Ч72 78Ч79 188
Bit: "Binary digit", either zero or unity      195 200
Bit: "Binary digit", random      12 30Ч32 35Ч36 38 48 119Ч120 170Ч176
Bitwise operations      see УBoolean operationsФ
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      30Ч31 140 202 328Ч329 389Ч390 459 605
Boolean operations, and      140 188 322 328Ч329 389Ч390 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      522Ч523
Borel, Emile Felix Edouard Justin      177
Borodin, Allan Bertram      498 505 515 707
Borosh, Itzhak      106Ч107 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 352Ч353 355 356 382 386 403 501 529Ч534 539Ч540 556 590 600 643 644 646 657 695 719Ч721
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 УSpencer BrownФ
Brown, George William      135
Brown, Mark Robbin      712
Brown, Robert      see УBrownian motionФ
Brown, William Stanley      419 428 438 454 686
Brownian motion      559
Bruijn, cycle      38Ч40
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      185Ч188 193 327 556
Cahen, Eugene      676
Calculating prodigies      279 295
Camion, Paul Frederic Roger      449
Campbell, Edward Fay, Jr.      vii.
1 2 3 4 5 6 7 8 9
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