Haar method

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11: 3 Numerical Methods

Chapter 3 Numerical Methods

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12: Amparo Gil

… ► Temme) of the book Numerical Methods for Special Functions, published by SIAM in 2007. … ►

3 Numerical Methods

13: Javier Segura

… ►Temme) of the book Numerical Methods for Special Functions, published by SIAM in 2007. … ►

3 Numerical Methods

14: 14.32 Methods of Computation

§14.32 Methods of Computation

… ►In other cases recurrence relations (§14.10) provide a powerful method when applied in a stable direction (§3.6); see Olver and Smith (1983) and Gautschi (1967). ►Other methods include: …

15: 1 Algebraic and Analytic Methods

Chapter 1 Algebraic and Analytic Methods

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16: 9.17 Methods of Computation

§9.17 Methods of Computation

… ►The former reference includes a parallelized version of the method. … ►In these cases boundary-value methods need to be used instead; see §3.7(iii). … ►The second method is to apply generalized Gauss–Laguerre quadrature (§3.5(v)) to the integral (9.5.8). For the second method see also Gautschi (2002a). …

17: 35.10 Methods of Computation

§35.10 Methods of Computation

… ►Other methods include numerical quadrature applied to double and multiple integral representations. …

18: 35.1 Special Notation

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$a,b$	complex variables.
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$\mathrm{d}𝐇$	normalized Haar measure on $𝐎(m)$.
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19: 27.19 Methods of Computation: Factorization

§27.19 Methods of Computation: Factorization

… ►Type I probabilistic algorithms include the Brent–Pollard rho algorithm (also called Monte Carlo method), the Pollard $p-1$ algorithm, and the Elliptic Curve Method (ecm). …As of January 2009 the largest prime factors found by these methods are a 19-digit prime for Brent–Pollard rho, a 58-digit prime for Pollard $p-1$, and a 67-digit prime for ecm. …

20: 7.22 Methods of Computation

§7.22 Methods of Computation

… ►The methods available for computing the main functions in this chapter are analogous to those described in §§6.18(i)–6.18(iv) for the exponential integral and sine and cosine integrals, and similar comments apply. … ►For a comprehensive survey of computational methods for the functions treated in this chapter, see van der Laan and Temme (1984, Ch. V).