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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Error bounds for linear recurrence relations

Author: F. W. J. Olver
Journal: Math. Comp. 50 (1988), 481-499
MSC: Primary 65Q05; Secondary 39A10, 65G05
MathSciNet review: 929547
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Abstract: Recurrence relations of the form

$\displaystyle {a_r}{p_{r + 1}} = {b_r}{p_r} + {c_r}{p_{r - 1}}$

are examined in two cases: (A) oscillatory systems, for which $ b_r^2 + 4{a_r}{c_r} < 0$; (B) monotonic systems, for which $ b_r^2 + 4{a_r}{c_r} \geq 0$. In both cases, a posteriori methods are supplied for constructing strict and realistic error bounds in $ O(r)$ arithmetic operations. A priori bounds, also requiring $ O(r)$ arithmetic operations, are supplied in Case B. Several illustrative numerical examples are included.

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PII: S 0025-5718(1988)0929547-9
Article copyright: © Copyright 1988 American Mathematical Society