Brent, R. P. (Richard P.)Overview
Most widely held works by
R. P Brent
Algorithms for minimization without derivatives
by R. P Brent
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Book
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17 editions published between 1972 and 2013 in English and held by 619 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
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Book
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12 editions published between 2010 and 2011 in English and held by 226 WorldCat member libraries worldwide "Modern Computer Arithmetic focuses on arbitraryprecision 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 highlevel description and avoiding too lowlevel or machinedependent details. The book is intended for anyone interested in the design and implementation of efficient highprecision algorithms for computer arithmetic, and more generally efficient multipleprecision 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
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Book
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2 editions published in 1976 in English and held by 101 WorldCat member libraries worldwide
Analysis of the binary Euclidean algorithm
by R. P Brent
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Book
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3 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 'latticepoint' model
Factorizations of Cunningham numbers with bases 13 to 99 : millennium edition
by R. P Brent
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Book
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4 editions published in 2001 in English and held by 10 WorldCat member libraries worldwide
Solving triangular systems on a parallel computer
by Ahmed Sameh
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Book
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2 editions published in 1975 in Undetermined and English and held by 9 WorldCat member libraries worldwide
Algorithms for finding zeros and extrema of functions without calculating derivatives
by R. P Brent
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Book
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5 editions published in 1971 in English and Undetermined and held by 8 WorldCat member libraries worldwide
Computation of the singular value decomposition using Meshconnected processors
by R. P Brent
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Book
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6 editions published between 1982 and 1983 in English and held by 8 WorldCat member libraries worldwide This paper concerns the systolic array computation of the generalized singular value decomposition. Numerical algorithms for both one and twodimensional systolic architectures are discussed
Improved techniques for lower bounds for odd perfect numbers
by R. P Brent
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Book
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4 editions published in 1989 in English and held by 7 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 areatime complexity of Binary multiplication
by R. P Brent
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Book
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3 editions published in 1979 in English and held by 7 WorldCat member libraries worldwide We consider the problem of performing multiplication of nbit 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)
A systolic algorithm for integer GCD computation
by R. P Brent
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Book
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3 editions published in 1984 in English and held by 7 WorldCat member libraries worldwide Abstract: "We show that the greatest common divisor of two nbit 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 finitestate machine with connections to its nearest neighbours."
A class of optimalorder zerofinding methods using derivative evaluations
by R. P Brent
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Book
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3 editions published in 1975 in English and held by 6 WorldCat member libraries worldwide It is often necessary to find an approximation to a simple zero zeta of a function f, using evaluations of f and f' . In this paper the author considers some methods which are efficient if f' is easier to evaluate than f . Examples of such functions are given
Numerically stable solution of dense systems of linear equations using meshconnected processors
by A Bojanczyk
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Book
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1 edition published in 1981 in English and held by 6 WorldCat member libraries worldwide
Factorizations of an̳ [plus over minus] 1, 13 [less than over minus] a [less than] 100
by R. P Brent
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Book
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5 editions published between 1992 and 1996 in English and held by 6 WorldCat member libraries worldwide
MP users guide
by R. P Brent
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Book
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3 editions published between 1976 and 1979 in English and held by 6 WorldCat member libraries worldwide
On the complexity of composition and generalized composition of power series
by R. P Brent
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Book
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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 (q1) (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
Computing the Cholesky factorization using a systolic architecture
by R. P Brent
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Book
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3 editions published in 1982 in English and held by 5 WorldCat member libraries worldwide This note concerns the computation of the Cholesky factorization of a symmetric and positive definite matrix on a systolic array. We use the special properties of the matrix to simplify the algorithm and the corresponding architecture given by Kung and Leiserson
The solution of singularvalue and symmetric eigenvalue problems on multiprocessor arrays
by R. P Brent
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Book
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3 editions published in 1983 in English and held by 5 WorldCat member libraries worldwide Key Words And Phrases: Multiprocessor arrays, systolic arrays, singularvalue decomposition, eigenvalue decomposition, real symmetric matrices, Hestenes method, Jacobi method, VLSI, realtime computation, parallel algorithms
Multipleprecision zerofinding methods and the complexity of elementary function evaluation
by R. P Brent
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Book
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3 editions published in 1975 in English and held by 5 WorldCat member libraries worldwide The author considers methods for finding highprecision approximations to simple zeros of smooth functions. As an application, the author gives fast methods for evaluating the elementary functions log(x), exp(x), sin(x) etc. to high precision. For example, if x is a positive floatingpoint number with an nbit fraction, then (under rather weak assumptions) an nbit approximation to log(x) or exp(x) may be computed in time asymptotically equal to 13M(n) log of n to the base 2 as n approaches infinity, where M(n) is the time required to multiply floatingpoint numbers with nbit fractions. Similar results are given for the other elementary functions, and some analogies with operations on formal power series are mentioned
Systolic array for the lineartime solution of Toeplitz systems of equations
by R. P Brent
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Book
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3 editions published in 1982 in English and held by 5 WorldCat member libraries worldwide The solution of an (n+1)x(n+1) Toeplitz system of linear equations on a onedimensional systolic architecture is studied. Our implementation of an algorithm due to Bareiss is shown to require only $O(n)$ time and $O(n)$ storage, i.e. constant storage per systolic processor more
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Algorithms Approximation theory Binary system (Mathematics) Computational complexityData processing Computer arithmetic Computer programming Equations, SimultaneousData processing Factorization (Mathematics)Data processing Functions Integrated circuitsVery large scale integration Iterative methods (Mathematics) Linear programming Linear systemsData processing Mathematical optimization MathematicsComputer programs MathematicsData processing MatricesData processing Maxima and minima Multiprocessors Number theory Number theoryData processing Numerical analysis Parallel processing (Electronic computers) Perfect numbers Polynomials Problem solving Roundoff errorsData processing Systolic array circuits

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 1946
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