forward series recurrence
♦
5 matching pages ♦
(0.002 seconds)
5 matching pages
1: 3.10 Continued Fractions
…
►
Forward Series Recurrence Algorithm
… ►This forward algorithm achieves efficiency and stability in the computation of the convergents , and is related to the forward series recurrence algorithm. …2: 16.25 Methods of Computation
…
►Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations.
…There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations).
…In these cases integration, or recurrence, in either a forward or a backward direction is unstable.
…
3: 2.9 Difference Equations
…
►Many special functions that depend on parameters satisfy a three-term linear recurrence relation
…
►
2.9.2
,
►in which is the forward difference operator (§3.6(i)).
►Often and can be expanded in series
…
►For asymptotic expansions in inverse factorial series see Olde Daalhuis (2004a).
…
4: 10.74 Methods of Computation
…
►
§10.74(i) Series Expansions
… ►In other circumstances the power series are prone to slow convergence and heavy numerical cancellation. … ►In the interval , needs to be integrated in the forward direction and in the backward direction, with initial values for the former obtained from the power-series expansion (10.2.2) and for the latter from asymptotic expansions (§§10.17(i) and 10.20(i)). … ►§10.74(iv) Recurrence Relations
… ►Then and can be generated by either forward or backward recurrence on when , but if then to maintain stability has to be generated by backward recurrence on , and has to be generated by forward recurrence on . …5: 11.13 Methods of Computation
…
►