61 citations · 445 across the 59 of their papers we have counts for
7 papers · 2 filters
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…
A weakly stable algorithm for general Toeplitz systems
Adam W. Bojanczyk, Richard P. Brent, Frank R. de Hoog
We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used…
On the stability of the Bareiss and related Toeplitz factorization algorithms
Adam W. Bojanczyk, Richard P. Brent, Frank R. de Hoog +1
This report contains a numerical stability analysis of factorization algorithms for computing the Cholesky decomposition of symmetric positive definite matrices of displacement ran…
An asymptotic expansion inspired by Ramanujan
Richard P. Brent
Corollary 2, Entry 9, Chapter 4 of Ramanujan's first notebook claims that a certain sum is asymptotic to ln(x) + gamma, where x is a real variable in the sum and gamma is Euler's c…
Unrestricted algorithms for elementary and special functions
Richard P. Brent
We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several gen…