61 citations · 445 across the 59 of their papers we have counts for
11 papers · 1 filter
On asymptotic approximations to the log-Gamma and Riemann-Siegel theta functions
Richard P. Brent
We give bounds on the error in the asymptotic approximation of the log-Gamma function for complex in the right half-plane. These improve on earlier bounds by Behnke a…
Asymptotic approximation of central binomial coefficients with rigorous error bounds
Richard P. Brent
We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of Pólya and Szegö, so the error incurred in t…
Bounds on determinants of perturbed diagonal matrices
Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith
We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix. The matrices conside…
A bound for the error term in the Brent-McMillan algorithm
Richard P. Brent, Fredrik Johansson
The Brent-McMillan algorithm B3 (1980), when implemented with binary splitting, is the fastest known algorithm for high-precision computation of Euler's constant. However, no rigor…
Multiple-precision zero-finding methods and the complexity of elementary function evaluation
Richard P. Brent
We consider methods for finding high-precision approximations to simple zeros of smooth functions. As an application, we give fast methods for evaluating the elementary functions l…
Error analysis of a partial pivoting method for structured matrices
Douglas R. Sweet, Richard P. Brent
Many matrices that arise in the solution of signal processing problems have a special displacement structure. For example, adaptive filtering and direction-of-arrival estimation yi…