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- J. M. Smith, F. W. J. Olver, Daniel W. Lozier
- ACM Trans. Math. Softw.
- 1981

An algorithm is presented for the computation of normalrzed Legendre polynomials. In order to permit wide ranges of argument, degree, and order of these functions, an "extended-range" arithmetic isâ€¦ (More)

- C. W. Clenshaw, F. W. J. Olver
- J. ACM
- 1984

A new number system is proposed for computer arithmetic based on iterated exponential functions. The mare advantage is to eradicate overflow and undertow, but there are several other advantages andâ€¦ (More)

- Daniel W. Lozier, Ronald F. Boisvert, +8 authors Charles Clark
- 2003

Daniel Lozier Qiming Wang (NIST ITL) Ronald Boisvert Charles Clark (NIST PL) Joyce Conlon Richard Askey (U. Wisconsin, Madison) Marjorie McClain Michael Berry (U. Bristol, UK) Bruce Fabijonas Walterâ€¦ (More)

- Adri B. Olde Daalhuis, F. W. J. Olver
- SIAM Review
- 1998

An investigation is made of the nature of asymptotic solutions of homogeneous linear differential equations of arbitrary order in the neighborhood of a singularity of unit rank. We introduce aâ€¦ (More)

- F. W. J. Olver
- 2010

Miller's algorithm is a device for computing the most rapidly decreasing solution of a second-order linear difference equation. In this paper strict upper bounds are given for the errors in theâ€¦ (More)

T rivia question: What is the most cited work in the mathematical literature? With an estimated 40,000 citations,1 the Handbook of Mathematical Functions [1] may well be it. Edited by Miltonâ€¦ (More)

- Bruce R. Fabijonas, F. W. J. Olver
- SIAM Review
- 1999

The general theories of the derivation of inverses of functions from their power series and asymptotic expansions are discussed and compared. The asymptotic theory is applied to obtain asymptoticâ€¦ (More)

- F. W. J. Olver, Peter R. Turner
- 1987 IEEE 8th Symposium on Computer Arithmeticâ€¦
- 1987

This paper is concerned with finding fast efficient algorithms for performing level-index arithmetic. The approach used combines the advantages of parallel processing with the use of table look-up.â€¦ (More)

- Bruce R. Fabijonas, Daniel W. Lozier, F. W. J. Olver
- ACM Trans. Math. Softw.
- 2004

We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods areâ€¦ (More)

- F. W. J. Olver
- 1987 IEEE 8th Symposium on Computer Arithmeticâ€¦
- 1987

Two closely related new systems of computer arithmetic are proposed. It is shown that both are closed under arithmetic operations in finite-precision arithmetic, thereby offering a permanent solutionâ€¦ (More)