Knuth, Donald E. The art of computer programming. Vol. 2: Seminumerical algorithms. 3rd ed. (English) Zbl 0895.65001 Bonn: Addison-Wesley. xiii, 762 p. (1998). [For a review of the 2nd edition (1981) see Zbl 0477.65002.]Publisher’s description: The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is the author’s new treatment of random number generators, and his discussion of calculations with formal power series. Cited in 5 ReviewsCited in 614 Documents MSC: 68-02 Research exposition (monographs, survey articles) pertaining to computer science 68W05 Nonnumerical algorithms 65Cxx Probabilistic methods, stochastic differential equations 65Gxx Error analysis and interval analysis 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis Keywords:random arithmetic; seminumerical algorithms; random numbers; computer programming; random number generators; formal power series; exercises; survey; linear congruence relations; statistical tests; spectral test; floating-point arithmetic; multiple-precision arithmetic; radix conversion; Euclidean algorithm; polynomial arithmetic Citations:Zbl 0477.65002; Zbl 0191.18001 PDFBibTeX XMLCite \textit{D. E. Knuth}, The art of computer programming. Vol. 2: Seminumerical algorithms. 3rd ed. Bonn: Addison-Wesley (1998; Zbl 0895.65001) Online Encyclopedia of Integer Sequences: Numbers n such that the smallest possible number of multiplications required to compute x^n is by 1 less than the number of multiplications obtained by Knuth’s power tree method. The power tree (as defined by Knuth), read by rows, where T(n,k) is the label of the k-th node in row n. Knuth’s power tree represented by parent node number.