backward recursion method

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1: 3.6 Linear Difference Equations

… ► … ►If, as

n\to\infty

, the wanted solution

w_{n}

grows (decays) in magnitude at least as fast as any solution of the corresponding homogeneous equation, then forward (backward) recursion is stable. …

2: 29.20 Methods of Computation

§29.20 Methods of Computation

… ►Subsequently, formulas typified by (29.6.4) can be applied to compute the coefficients of the Fourier expansions of the corresponding Lamé functions by backward recursion followed by application of formulas typified by (29.6.5) and (29.6.6) to achieve normalization; compare §3.6. … ►A third method is to approximate eigenvalues and Fourier coefficients of Lamé functions by eigenvalues and eigenvectors of finite matrices using the methods of §§3.2(vi) and 3.8(iv). …The numerical computations described in Jansen (1977) are based in part upon this method. ►A fourth method is by asymptotic approximations by zeros of orthogonal polynomials of increasing degree. …

3: 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. … ►The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing

\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(x\right)

. See Gautschi (1977a), where forward and backward recursions are used; see also Gautschi (1961). … ►For a comprehensive survey of computational methods for the functions treated in this chapter, see van der Laan and Temme (1984, Ch. V).