Richard Peirce Brent ( born April 20, 1946, Melbourne ) is an Australian mathematician and computer scientist , emeritus professor at the Australian National University and professor at the in Australia. From March 2005 to March 2010 he received a federal scholarship from the Australian government, designed to retain highly qualified specialists in the country [2] . He works in the areas of development of computational algorithms, number theory , factorization , pseudo-random sequence generation , computer architecture and algorithm analysis .
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| Scientific field | Maths |
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| Awards and prizes | [d] ( 1995 ) [d] [d] [d] |
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In 1970, Brent reduced the problem of finding a bilinear algorithm for quickly multiplying matrices such as the Strassen algorithm to solving the system of cubic Brent equations. [3] .
In 1973, he published a highly accurate combined method for numerically solving equations that does not require the calculation of the derivative, and subsequently became popular as . [four]
In 1975, he and independently developed, based on algorithm, the Salamin-Brent algorithm used to calculate the number . Brent proved that all elementary functions , in particular, log ( x ) and sin ( x ) can be calculated with a given accuracy in a time of the same order as the number method using the arithmetic-geometric mean of Karl Friedrich Gauss . [five]
In 1979, Brent showed that the first 75 million complex zeros of the Zeta Riemann function lie on a critical line in accordance with the Riemann hypothesis . [6]
In 1980, Brent and Nobel laureate Edwin McMillan found a new algorithm for highly accurate calculation of the Euler-Maskeroni constant using Bessel functions , and showed that can be a rational number p / q only if the integer q is greater than 10 15000 [7] .
In 1980, Brent and factorized the eighth Fermat number using the modified Pollard Ρ-algorithm . [8] Subsequently, Brent factorized the tenth [9] and eleventh Fermat numbers using the factorization algorithm using elliptic curves .
In 2002, Brent, Samuli Larwala and Paul Zimerman discovered very large primitive trinomials over the Galois field GF (2):
The degree of the trinomial 6972593 is an exponent in the Mersenne prime number . [ten]
In 2009, Brent and Zimmerman discovered a primitive trinomial:
The number 43112609 is also an exponent in the Mersenne prime number. [eleven]
In 2010, Brent and Zimmerman published a book on arithmetic algorithms for modern computers - Modern Computer Arithmetic, (Cambridge University Press, 2010).
Brent is a member of the Computer Science Association , IEEE , , and the Australian Academy of Sciences . In 2005, the Australian Academy of Sciences awarded Brent .
Notes
- ↑ 1 2 3 German National Library , Berlin State Library , Bavarian State Library , etc. Record # 143984713 // General regulatory control (GND) - 2012—2016.
- ↑ Federation Fellowships Funding Outcomes 2004 Archived July 7, 2012 to Wayback Machine . Australian research council
- ↑ RP Brent, Algorithms for matrix multiplications, Comput. Sci. Dept. Report CS 157 (Stanford Univ., 1970)
- ↑ Brent, 1973 .
- ↑ Brent, 1976 .
- ↑ Brent, 1979 .
- ↑ Brent, McMillan, 1980 .
- ↑ Brent, Pollard, 1981 .
- ↑ Brent, 1999 .
- ↑ Brent, Larvala, Zimmermann, 2005 .
- ↑ Brent, Zimmermann, 2011 .
Articles
- Brent R. P. Algorithms for Minimization without Derivatives - Englewood Cliffs : Prentice Hall , 1973. - 195 p. - ISBN 978-0-13-022335-7
- Brent R. P. Multiple-Precision Zero-Finding Methods and the Complexity of Elementary Function Evaluation // Analytic Computational Complexity / J. F. Traub - Academic Press , 1976. - P. 151–176. - 250 p. - doi: 10.1016 / B978-0-12-697560-4.50014-9 - arXiv: 1004.3412
- Brent R. P. On the Zeros of the Riemann Zeta Function in the Critical Strip // Math. Comp. - AMS , 1979. - Vol. 33, Iss. 148. - P. 1361–1372. - ISSN 0025-5718 ; 1088-6842 - doi: 10.1090 / S0025-5718-1979-0537983-2
- Brent R. P. , McMillan E. M. Some New Algorithms for High-Precision Computation of Euler's Constant // Math. Comp. AMS 1980. Vol. 34, Iss. 149. - P. 305-312. - ISSN 0025-5718 ; 1088-6842 - doi: 10.1090 / S0025-5718-1980-0551307-4
- Brent R. P. , Pollard J. M. Factorization of the Eighth Fermat Number // Math. Comp. AMS , 1981. Vol. 36, Iss. 154. - P. 627-630. - ISSN 0025-5718 ; 1088-6842 - doi: 10.1090 / S0025-5718-1981-0606520-5
- Brent R. P. Factorization of the Tenth Fermat Number // Math. Comp. AMS 1999. Vol. 68, Iss. 225. - P. 429–451. - ISSN 0025-5718 ; 1088-6842 - doi: 10.1090 / S0025-5718-99-00992-8
- Brent R. P. , Larvala S. , Zimmermann P. A primitive trinomial of degree 6972593 // Math. Comp. - AMS , 2005 .-- Vol. 74, Iss. 250. - P. 1001-1002. - ISSN 0025-5718 ; 1088-6842 - doi: 10.1090 / S0025-5718-04-01673-4
- Brent R. P. , Zimmermann P. The Great Trinomial Hunt // Notices Amer. Math. Soc. / F. Morgan - AMS , 2011 .-- Vol. 58. - P. 233–239. - ISSN 0002-9920 - arXiv: 1005.1967