Richard P. Brent

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Richard Peirce Brent (born April 20, 1946 in Melbourne ) is an Australian mathematician ( numerical mathematics ) and computer scientist .

Life

Brent studied at Monash University (bachelor's degree in mathematics 1968) and Stanford University (master's degree in computer science in 1970), where he received his doctorate in numerical mathematics in 1971 under George Forsythe (1917–1972) and Gene Golub ( Algorithms for finding zeros and extrema of functions without calculating derivatives ). He also received a Masters Degree from Oxford University in 1998 and a PhD (D.Sc.) in Computer Science from Monash University in 1981. As a post-doc he was at IBM in Yorktown Heights in 1971/72 . From 1972 to 1976 he was a researcher at the Computer Center of the Australian National University (ANU), where he was Professor of Computer Science from 1978 and from 1985 headed the Computer Science Lab. From 1998 to 2005 he was Professor of Computer Science at Oxford University and a Fellow of St. Hugh's College. Since 2005 he has been an Australian Research Council (ARC) Fellow at ANU at the ARC Center of Excellence for Mathematics and Statistics of Complex Systems . Among other things, he was visiting professor in the 1970s at Stanford University, Carnegie Mellon University and the University of California, Berkeley, and in 1997 at Harvard .

In 1963 he received the Australian BHP Prize. Since 1982 he has been a member of the Australian Academy of Sciences , whose Hannan Medal he received in 2005. In 1984 he received the Medal of the Australian Mathematical Society . He is a fellow of the British Computer Society and the Association for Computing Machinery (ACM).

plant

Brent deals with complexity theory , algorithmic number theory , analysis of algorithms, neural networks, random algorithms, high-precision arithmetic, random number generators, parallel and distributed computing and cryptography .

For example, he was concerned with calculating the zeros of the Riemann zeta function (and showed that the first 75 million zeros lie on the critical straight line) and factored the eighth Fermat number with John M. Pollard and the tenth in 1999 and the eleventh in 1988 (both with Hendrik Lenstra's Elliptic Curve Factoring Method). An algorithm published by him in 1973 ( Brent method ) for the numerical determination of zeros of functions is named after him. In 1975, independently of Eugene Salamin, he found the Brent-Salamin algorithm for determining pi (with a method that goes back to Carl Friedrich Gauß and Legendre and uses the arithmetic-geometric mean ), and also showed that the elementary functions (such as sine, Cosine, logarithm) can be evaluated with high accuracy with the same complexity as pi. His collection of Fortran routines MP (1978) for numerical computation and for the evaluation of elementary functions with selectable high accuracy was widely used because it was freely accessible and particularly efficient with increasing numbers of digits. In 1980 he and Edwin McMillan found a new algorithm for determining the Euler-Mascheroni constant with the help of Bessel functions .

Most recently he worked with Paul Zimmermann on a book on modern computer arithmetic, the preliminary version of which can be accessed online.

Fonts

  • Algorithms for minimization without derivatives , Prentice-Hall 1973, ISBN 0-13-022335-2 ; Dover Publications 2002, ISBN 0-486-41998-3 .
  • with Paul Zimmermann: Modern computer arithmetic. (Cambridge Monographs on Applied and Computational Mathematics, No. 18) Cambridge University Press 2010, ISBN 0-521-19469-5 .

See also

Web links

Individual evidence

  1. ↑ On the zeros of the Riemann zeta function on the critical strip , Math. Of Computation, Volume 33, 1979, p. 1361, Volume 39, 1981, p. 681
  2. ↑ Brent, Pollard: Factorization of the eighth Fermat number , Math. Of Computation, Volume 36, 1981, p. 627
  3. ^ Math. Of Computation, Volume 69, 1999, p. 429
  4. ↑ Brent to factorize F11
  5. ^ Salamin: Computation of Pi using arithmetic-geometric mean , Math. Of Computation, Volume 30, 1976, p. 565. In addition Brent-Salamin formula in Math World
  6. ↑ Brent: Multiple precision zero finding methods and the complexity of elementary function evaluation , in Traub (editor): Analytic computational complexity , Academic Press 1975
  7. ^ Brent: A Fortran Multiple-Precision Arithmetic Package. ACM Transact. Math. Software, Vol. 4 (1978), No. 1, pp. 57-70
  8. ↑ Brent: Fast Multiple Precision Evaluation of Elementary Functions. Journal of the ACM, Vol. 23 (1976), pp. 242-251
  9. ↑ Brent, McMillan: Some new algorithms for high precision calculation of Euler's constant , Math. Of Computation, Volume 34, 1980, pp. 305-312
  10. ↑ Description and URL of Modern Computer Arithmetic
personal data
SURNAME Brent, Richard P
ALTERNATIVE NAMES Brent, Richard Peirce
BRIEF DESCRIPTION Australian mathematician
DATE OF BIRTH April 20, 1946
PLACE OF BIRTH Melbourne