Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65Q05, 39A10, 65G05

Retrieve articles in all journals with MSC: 65Q05, 39A10, 65G05

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society