The Art of Computer Programming, Volume 2: Seminumerical Algorithms

Knuth, D. E. (1997). The Art of Computer Programming, Volume 2: Seminumerical Algorithms: Seminumerical Algorithms. Addison-Wesley.

Type

Book

Intellectual base

Textbook

Year

1997

Volume

2

ISBN

9780201896848

Link

https://openlibrary.org/isbn/9780201896848

Cited from

mathematics

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Equivalence Relation
  • An equivalence relation is not the same as equality-up-to-some-error-bound, the failure mode Knuth (1997) analyses in the seminumerical-algorithms context where floating-point ε-equality is reflexive and symmetric but not transitive.

    This sourceTreats floating-point representation and arithmetic, where ε-equality (|a−b| < ε) is reflexive and symmetric but not transitive (small ε-close chains accumulate to large gaps). (Citation-fix: the prime cited 'Volume 1: Fundamental Algorithms', but floating-point/seminumerical material — which the prose itself names — is Volume 2; the prior annotation about 'recurrence relations' also described Volume 1 and was mismatched to this claim.)

Domain-specific

• Division (mathematics)
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Pseudorandom Number Generator
  • “Random” therefore describes selected output properties or adversarial indistinguishability, not nondeterministic causation.
• Random number generation
  • Random number generation is the process of producing a sequence of numbers or symbols under a stated randomness model, using physical sampling, pseudorandom algorithms, or a qualified combination of entropy acquisition and deterministic expansion.
• Randomness Test
  • Report the number of tests, dependence among them, multiplicity policy, sample sizes, and expected false-rejection rate.

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