WorldCat Identities

Brent, R. P. (Richard P.)

Overview
Works: 90 works in 194 publications in 1 language and 1,113 library holdings
Roles: Thesis advisor
Classifications: QA402.5, 515.33
Publication Timeline
Key
Publications about  R. P Brent Publications about R. P Brent
Publications by  R. P Brent Publications by R. P Brent
Most widely held works by R. P Brent
Algorithms for minimization without derivatives by R. P Brent ( Book )
16 editions published between 1972 and 2013 in English and held by 537 WorldCat member libraries worldwide
Outstanding text for graduate students and research workers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. Many numerical examples, along with complete analysis of rate of convergence for most of the algorithms and error bounds that allow for the effect of rounding errors
Modern computer arithmetic by R. P Brent ( Book )
12 editions published between 2010 and 2011 in English and held by 222 WorldCat member libraries worldwide
"Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favorite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors."--Publisher's website
The Complexity of computational problem solving ( Book )
3 editions published in 1976 in English and held by 100 WorldCat member libraries worldwide
Algorithms for finding zeros and extrema of functions without calculating derivatives by R. P Brent ( Book )
7 editions published in 1971 in English and Undetermined and held by 10 WorldCat member libraries worldwide
Theorems are given concerning the order (i.e., rate) of convergence of a successive interpolation process for finding simple zeros of a function or its derivatives, using only function evaluations. Special cases include the successive linear interpolation process for finding zeros, and a parabolic interpolation process for finding turning points. Results on interpolation and finite differences include weakening the hypotheses of a theorem of Ralston on the derivative of the error in Lagrangian interpolation. The theoretical results are applied to given algorithms for finding zeros or local minima of functions of one variable, in the presence of rounding errors. The algorithms are guaranteed to converge nearly as fast as would bisection or Fibonacci search, and in most practical cases convergence is superlinear, and much faster than for bisection or Fibonacci search. (Author)
Analysis of the binary Euclidean algorithm by R. P Brent ( Book )
2 editions published in 1976 in English and held by 10 WorldCat member libraries worldwide
In this paper the author analyzes a continuous model of the binary algorithm and finds the expected number of iterations. The results agree with the observed behavior of the algorithm much better than those predicted by Knuth's 'lattice-point' model
Factorizations of a[superscript n] [+ or -] 1, 13 [<or =] a <100 by R. P Brent ( Book )
6 editions published between 1992 and 1996 in English and held by 9 WorldCat member libraries worldwide
Abstract: "As an extension of the 'Cunningham' tables, we present tables of factorizations of a[superscript n] [+ or -] 1 for 13 [<or =] a <100. The exponents n satisfy a[superscript n] <10²⁵⁵if a <30, and n [<or =] 100 if a [> or =] 30. The factorizations are complete for n [<or =] 46, and the tables contain no composite numbers smaller than 10⁸⁰."
Solving triangular systems on a parallel computer by Ahmed Sameh ( Book )
2 editions published in 1975 in Undetermined and English and held by 9 WorldCat member libraries worldwide
A systolic algorithm for integer GCD computation by R. P Brent ( Book )
7 editions published between 1982 and 1984 in English and Undetermined and held by 9 WorldCat member libraries worldwide
Abstract: "We show that the greatest common divisor of two n-bit integers (given in the usual binary representation) can be computed in time O(n) on a linear array of O(n) identical systolic cells, each of which is a finite-state machine with connections to its nearest neighbours."
Factorizations of Cunningham numbers with bases 13 to 99 : millennium edition by R. P Brent ( Book )
3 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide
Improved techniques for lower bounds for odd perfect numbers by R. P Brent ( Book )
6 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
Abstract: "If N is an odd perfect number, and q[superscript k] [symbol] N, q prime, k even, then it is almost immediate that N> q[superscript 2k]. We prove here that, subject to certain conditions verifiable in polynomial time, in fact N> q[superscript 5k/2]. Using this and related results, we are able to extend the computations in an earlier paper to show that N> 10[superscript 300]."
The area-time complexity of Binary multiplication by R. P Brent ( Book )
3 editions published in 1979 in English and Undetermined and held by 7 WorldCat member libraries worldwide
We consider the problem of performing multiplication of n-bit binary numbers on a chip. Let A denote the chip area, and T the time required to perform multiplication. Using a model of computation which is a realistic approximation to current and anticipated VLSI technology, we show that (A/A sub 0) (T/T sub 0) to the 2 alpha power> or = n to the (1 + alpha) power for all alpha is an element (0, 1), where A sub 0 and T sub 0 are positive constants which depend on the technology but are independent of n. The exponent 1 + alpha is the best possible. A consequence is that binary multiplication is 'harder' than binary addition if AT to the 2 alpha power is used as a complexity measure for any alpha> or = 0. (Author)
Computation of the generalized singular value decomposition using mesh-connected processors by R. P Brent ( Book )
5 editions published between 1982 and 1983 in English and held by 7 WorldCat member libraries worldwide
This paper concerns the systolic array computation of the generalized singular value decomposition. Numerical algorithms for both one and two-dimensional systolic architectures are discussed
On the complexity of composition and generalized composition of power series by R. P Brent ( Book )
2 editions published in 1978 in English and held by 6 WorldCat member libraries worldwide
Let F(x) = f1x + f2(x)(x) + ... be a formal power series over a field Delta. Let F superscript 0(x) = x and for q = 1,2, ..., define F superscript q(x) = F superscript (q-1) (F(x)). The obvious algorithm for computing the first n terms of F superscript q(x) is by the composition position analogue of repeated squaring. This algorithm has complexity about log 2 q times that of a single composition. The factor log 2 q can be eliminated in the computation of the first n terms of (F(x)) to the q power by a change of representation, using the logarithm and exponential functions. We show the factor log 2 q can also be eliminated for the composition problem. F superscript q(x) can often, but not always, be defined for more general q. We give algorithms and complexity bounds for computing the first n terms of F superscript q(x) whenever it is defined
A regular layout for parallel adders by R. P Brent ( Book )
3 editions published in 1979 in English and held by 6 WorldCat member libraries worldwide
With VLSI architecture the chip area is a better measure of cost than the conventional gate count. We show that addition of n-bit binary numbers can be performed on a chip in time proportional to log n and with area proportional to n log n. (Author)
On the zeros of the Riemann zeta function in the critical strip by R. P Brent ( Book )
4 editions published between 1976 and 1982 in English and held by 6 WorldCat member libraries worldwide
Numerically stable solution of dense systems of linear equations using mesh-connected processors by A Bojanczyk ( Book )
2 editions published in 1981 in English and held by 6 WorldCat member libraries worldwide
The solution of singular value problems using systolic arrays by R. P Brent ( Book )
4 editions published in 1984 in English and held by 5 WorldCat member libraries worldwide
This paper contains the computation of the singular value decomposition using systolic arrays. Two different linear time algorithms are presented
MP users guide by R. P Brent ( Book )
2 editions published between 1976 and 1978 in English and held by 5 WorldCat member libraries worldwide
A Fortran multiple-precision arithmetic package by R. P Brent ( Book )
1 edition published in 1976 in English and held by 5 WorldCat member libraries worldwide
Fast algorithms for manipulating formal power series by R. P Brent ( Book )
2 editions published in 1976 in English and held by 5 WorldCat member libraries worldwide
The classical algorithms require O(n sup 3) operations to compute the first n terms in the reversion of a power series or the composition of two series, and O((n sup 2) log n) operations if the fast Fourier transform is used for power series multiplication. In this paper we show that the composition and reversion problems are equivalent (up to constant factors), and we give algorithms which require only O((n log n) sup 3/2) operations. In many cases of practical importance only O(n log n) operations are required. An application to root-finding methods which use inverse interpolation is described, some results on multivariate power series are stated, and several open questions are mentioned
 
moreShow More Titles
fewerShow Fewer Titles
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.72 (from 0.47 for Computatio ... to 0.92 for Numericall ...)
Alternative Names
Brent, R. 1946-
Brent, R. P.
Brent, R. P. 1946-
Brent, Richard
Brent, Richard 1946-
Brent, Richard P.
Brent, Richard P., 1946-
Brent, Richard Peirce
Brent, Richard Peirce 1946-
Languages
English (88)
Covers