Education
Australian National University.
( This outstanding text for graduate students and researc...)
This outstanding text for graduate students and researchers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. None of the algorithms requires an evaluation of derivatives; all depend entirely on sequential function evaluation, a highly practical scenario in the frequent event of difficult-to-evaluate derivatives. Topics include the use of successive interpolation for finding simple zeros of a function and its derivatives; an algorithm with guaranteed convergence for finding a minimum of a function of one variation; global minimization given an upper bound on the second derivative; and a new algorithm for minimizing a function of several variables without calculating derivatives. Many numerical examples augment the text, along with a complete analysis of rate of convergence for most algorithms and error bounds that allow for the effect of rounding errors.
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mathematician university professor computer scientist
Australian National University.
He is an emeritus professor at the Australian National University and a conjoint professor at the University of Newcastle (Australia). From March 2005 to March 2010 he was a Federation Fellow at the Australian National University. His research interests include number theory (in particular factorisation), random number generators, computer architecture, and analysis of algorithms.
In 1973, he published a root-finding algorithm (an algorithm for solving equations numerically) which is now known as Brent"s method.
In 1975 he and Eugene Salamin independently conceived the Salamin–Brent algorithm, used in high-precision calculation of. At the same time, he showed that all the elementary functions (such as log(x), sin(x) et cetera) can be evaluated to high precision in the same time as (apart from a small constant factor) using the arithmetic-geometric mean of Carl Friedrich Gauss.
In 1979 he showed that the first 75 million complex zeros of the Riemann zeta function lie on the critical line, providing some experimental evidence for the Riemann hypothesis. In 1980 he and Nobel laureate Edwin McMillan found a new algorithm for high-precision computation of the Euler–Mascheroni constant using Bessel functions, and showed that can not have a simple rational form p/q (where p and q are integers) unless q is extremely large (greater than 1015000).
In 1980 he and John Pollard factored the eighth Fermat number using a variant of the Pollard rho algorithm.
He later factored the tenth and eleventh Fermat numbers using Lenstra"s elliptic curve factorisation algorithm. In 2002, Brent, Samuli Larvala and Paul Zimmermann discovered a very large primitive trinomial over GF(2):
The degree 43112609 is again the exponent of a Mersenne prime. In 2010, Brent and Paul Zimmermann published "Modern Computer Arithmetic", (Cambridge University Press, 2010), a book about algorithms for performing arithmetic, and their implementation on modern computers.
Brent is a Fellow of the Association for Computing Machinery, the Institute of Electrical and Electronics Engineers, Society for Industrial and Applied Mathematics and the Australian Academy of Science.
In 2005, he was awarded the Hannan Medal by the Australian Academy of Science.
( This outstanding text for graduate students and researc...)