Alex au pays des chiffres - download pdf or read online

By Alex Bellos

ISBN-10: 2221122933

ISBN-13: 9782221122938

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1. For a treatment of stability aspects of more general difference equations, and systems thereof, including nonlinear ones, the reader is referred to the monograph by Wimp [1984]. This also contains many applications to special functions. Other relevant texts are Lakshmikantham and Trigiante [2002] and Elaydi [2005]. 2. The condition of algebraic equations, although considered already in 1963 by Wilkinson, has been further analyzed by Gautschi [1973]. 56), which he himself describes as “the most traumatic experience in [his] career as a numerical analyst,” are related in the essay Wilkinson [1984, Sect.

B/ D maxn b2R b¤0 x 2R x ¤0 kAxk kA 1 k D kAk kA kxk 1 k; by definition of the norm of A. , on b) and is called the condition number of the matrix A. 59) It should be clearly understood, though, that it measures the condition of a linear system with coefficient matrix A, and not the condition of other quantities that may depend on A, such as eigenvalues. 59) is also relevant when perturbations in the matrix A are allowed, provided they are sufficiently small (so small, for example, that kAk kA 1 k < 1).

5) Here all bi and cj are binary digits, that is, either zero or one. The binary fraction f is usually referred to as the mantissa of x and the integer e as the exponent of x. 4) is said to be normalized if in its fraction f we have b 1 D 1. t; s/ are normalized (with the exception of x D 0, which is treated as a special number). If x ¤ 0 were not normalized, we could 4 1 Machine Arithmetic and Related Matters f ± b −1 b −2 t e ··· b −t ± c s−1 bits c s−2 s ··· c0 bits Fig. 1 Packing of a floating-point number in a machine register multiply f by an appropriate power of 2, to normalize it, and adjust the exponent accordingly.

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Alex au pays des chiffres by Alex Bellos

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