Professor Richard Brent
BSc DSc *Monash* MS PhD *Stanford* MA *Oxon* FAA FACM FIEEE FIMA FAustMS FSIAM
Emeritus Professor
ANU College of Science
Areas of expertise
- Algebra And Number Theory 010101
- Analysis Of Algorithms And Complexity 080201
- Numerical And Computational Mathematics 0103
Biography
Research interests:
Analysis of algorithms, computational complexity, computational number theory, parallel/distributed computing, randomised algorithms, random number generators, scientific computing.
Duties:
He is an Emeritus Professor associated with the Mathematical Sciences Institute and the Research School of Computer Science at the Australian National University.
Publications
- Brent, R, Platt, D & Trudgian, T 2021, 'Accurate estimation of sums over zeros of the riemann zeta-function', Mathematics of Computation, vol. 90, no. 332, pp. 2923-2935.
- Brent, R, POMERANCE, C, PURDUM, D et al. 2021, 'Algorithms for the Multiplication Table Problem', Integers, vol. 21, pp. #A92.
- Brent, R, Platt, D & Trudgian, T 2021, 'The mean square of the error term in the prime number theorem', Journal of Number Theory, vol. 238, pp. 740-762.
- Brent, R 2021, 'On two theorems of Vassilev-Missana', Notes on Number Theory and Discrete Mathematics, vol. 27, no. 2, pp. 49-50.
- Brent, R, Platt, D & Trudgian, T 2020, 'A HARMONIC SUM over NONTRIVIAL ZEROS of the RIEMANN ZETA-FUNCTION', Bulletin of the Australian Mathematical Society, vol. online.
- Brent, R 2020, 'The borwein brothers, pi and the AGM', in D Bailey, N Borwein, R Brent, R Burachik, J Osborn, B Sims & Q Zhu (ed.), From Analysis to Visualization: A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017, Springer, Cham, pp. 323-347.
- Brent, R 2019, 'On the Accuracy of Asymptotic Approximations to the Log-Gamma and Riemann-Siegel Theta Functions', Journal of the Australian Mathematical Society, vol. 107, no. 3, pp. 319-337.
- Brent, R, Glasser, M & Guttmann , A 2019, 'A Conjectured Integer Sequence Arising From the Exponential Integral', Journal of Integer Sequences, vol. 22, no. 4, pp. 1-18.
- Brent, R & Yedidia, A 2018, 'Computation of Maximal Determinants of Binary Circulant Matrices', Journal of Integer Sequences, vol. 21, no. 5, pp. 1-19.
- Bailey, D, Borwein, J, Brent, R et al 2017, 'Reproducibility in Computational Science: A Case Study: Randomness of the Digits of Pi', Experimental Mathematics, vol. 26, no. 3, pp. 298-305pp.
- Brent, R, Krattenthaler, C & Warnaar, O 2016, 'Discrete analogues of Macdonald–Mehta integrals', Journal of Combinatorial Theory Series A, vol. 144, no. -, pp. 80-138.
- Brent, R, Osborn, J & Smith, W 2016, 'Probabilistic lower bounds on maximal determinants of binary matrices', Australasian Journal of Combinatorics, vol. 66, no. 3, pp. 350-364.
- Brent, R & Johansson, F 2015, 'A bound for the error term in the Brent-McMillan algorithm', Mathematics of Computation, vol. 84, no. 295, pp. 2351-2359.
- Bai, S, Brent, R & Thome, E 2015, 'Root optimization of polynomials in the number field sieve', Mathematics of Computation, vol. 84, no. 295, pp. 2447-2457.
- Brent, R, Osborn, J & Smith, W 2015, 'Note on best possible bounds for determinants of matrices close to the identity matrix', Linear Algebra and its Applications, vol. 466, pp. 21-26.
- Brent, R 2015, 'Generalizing Tuenter's binomial sums', Journal of Integer Sequences, vol. 18, no. 3, pp. 1-9.
- Brent, R, Osborn, J & Smith, W 2014, 'Bounds on determinants of perturbed diagonal matrices', arXiv (e-archive for Pre-prints, author submits), no. 1401.7084v7.
- Brent, R, Osborn, J & Smith, W 2014, 'Lower bounds on maximal determinants of binary matrices via the probabilistic method', arXiv (e-archive for Pre-prints, author submits), no. 1402.6817v2.
- Brent, R, Ohtsuka, H, Osborn, J et al 2014, 'Some binomial sums involving absolute values', arXiv (e-archive for Pre-prints, author submits), no. 1411.1477v1.
- Brent, R & Osborn, J 2013, 'Bounds on minors of binary matrices', Bulletin of the Australian Mathematical Society, vol. 88, no. 2, pp. 280-285.
- Brent, R & Osborn, J 2013, 'On Minors of Maximal Determinant Matrices', Journal of Integer Sequences, vol. 16, no. 4.
- Brent, R & Osborn, J 2013, 'General lower bounds on maximal determinants of binary matrices', Electronic Journal of Combinatorics, vol. 20, no. 2, p. 12.
- Brent, R 2013, 'Finding D-optimal designs by randomised decomposition and switching', Australasian Journal of Combinatorics, vol. 55, pp. 15-30.
- Arias de Reyna, J, Brent, R & Lune, J 2013, 'On the sign of the real part of the Riemann zeta-function', in J.M Borwein (ed.), Number Theory and Related Fields: In Memory of Alf van der Poorten, Springer, Online, pp. 75-97.
- Brent, R 2013, 'Old and new algorithms for pi', Notices of the American Mathematical Society, vol. 60, no. 1, p. 7.
- Nandapalan, N, Brent, R, Murray, L et al 2012, 'High-performance pseudo-random number generation on graphics processing units', International Conference on Parallel Processing and Applied Mathematics (PPAM 2011), Springer, Torun Poland, pp. 609-618.
- Brent, R, Arias de Reyna, J & Lune, J 2011, 'A note on the real part of the Riemann zeta-function', in J van de Lune (ed.), Herman J. J. te Riele Liber Amicorum, Centrum voor Wiskunde en Informatica, Amsterdam, pp. 8-14.
- Brent, R & Lune, J 2011, 'A note on Polya's observation concerning Liouville's function', in J van de Lune (ed.), Herman J. J. te Riele Liber Amicorum, Centrum voor Wiskunde en Informatica, Amsterdam, pp. 2-7.
- Brent, R & Harvey, D 2011, 'Fast Computation of Bernoulli, Tangent and Secant Numbers', Workshop on Computational and Analytical Mathematics in honour of Jonathan Borwein's 60th birthday, Springer, Berlin Germany, p. 16.
- Brent, R & Zimmermann, P 2011, 'The great trinomial hunt', Notices of the American Mathematical Society, vol. 58, no. 2, pp. 233-239.
- Brent, R & Zimmermann, P 2009, 'Ten New Primitive Binary Trinomials', Mathematics of Computation, vol. 78, no. 266, pp. 1197-1199.
- Brent, R & Zimmermann, P 2010, 'An O(M (n) log n) Algorithm for the Jacobi Symbol', Algorithmic Number Theory International Symposium (ANTS 2010), ed. Guillaume Hanrot et al, Springer, New York, pp. 83-95.
- Brent, R 2006, 'Some long-period random number generators using shifts and xors', ANZIAM Journal, vol. 48, pp. 188-202.
- Brent, R 2008, 'Some Comments on C. S. Wallace's Random Number Generators', The Computer Journal, vol. 51, no. 5, pp. 579-584.
- Brent, R & Zimmermann, P 2008, 'A Multi-level Blocking Distinct-degree Factorization Algorithm', Contemporary Mathematics, vol. 461, pp. 47-58.
- Brent, R, Gaudry, P & Zimmermann, P 2008, 'Faster Multiplication in GF(2)[x]', Algorithmic Number Theory International Symposium (ANTS 2008), ed. A. J. van der Poorten and A. Stein, Springer, Berlin, Germany.
- Brent, R, Gao, S & Lauder, A 2003, 'Random krylov spaces over finite fields', SIAM Journal on Discrete Mathematics, vol. 16, no. 2, pp. 276-287.
- Bai, S & Brent, R 2008, 'On the efficiency of Pollard's Rho method for discrete logarithms', Conferences in Research and Practice in Information Technology - CRPIT, vol. 77, pp. 125-131.
- Liang, W, Brent, R, Xu, Y et al 2009, 'Minimum-Energy All-to-All Multicasting in Wireless Ad Hoc Networks', IEEE Transactions on Wireless Communications, vol. 8, no. 11, pp. 5490-5499.
- Wang, P, Zhou, B, Taraeneh, M et al 2007, 'A global maximum likelihood super-quartet phylogeny method', Asia-Pacific Bioinformatics Conference (APBC 2007), ed. David Sankoff, Lusheng Wang, Francis Chin, Imperial College Press, London, UK, pp. 373-381.
- Lui, Y, Brent, R & Calinescu, A 2007, 'Extracting significant phrases from text', International Conference on Advanced Information Networking and Applications (AINAW 2007), ed. Conference Program Committee, Institute of Electrical and Electronics Engineers (IEEE Inc), New York, pp. 361-366.
- Brent, R, Percival, C & Zimmermann, P 2007, 'Error bounds on complex floating-point multiplication', Mathematics of Computation, vol. 76, pp. 1469-1481.
- Brent, R 2006, 'Fast algorithms for high-precision computation of elementary functions', Real Numbers and Computers Conference 2006, ed. Paul Zimmermann and Guillaume Hanro, Nancy Universite, Nancy France, pp. 7-11.
- Brent, R 2006, 'Fast and Reliable Random Number Generators for Scientific Computing', Workshop on the State-of-the-Art in Scientific Computing 2004, ed. Conference Program Committee, Conference Organising Committee, Berlin, pp. 1-10.
- Zhou, B, Chu, D, Tarawmeh, M et al 2006, 'Parallel implementation of a quartet-based algorithm for phylogenetic analysis', International Parallel and Distributed Processing Symposium (IPDPS 2006), ed. Conference Program Committee, Institute of Electrical and Electronics Engineers (IEEE Inc), online, pp. 8-16.
- Zhou, B, Tarawmeh, M, Wang, P et al 2006, 'Evidence of Multiple Maximum Likelihood Points for a Phylogenetic Tree', IEEE Symposium on BionInformatics and BioEngineering (BIBE 2006), ed. Conference Program Committee, Institute of Electrical and Electronics Engineers (IEEE Inc), United States, pp. 193-200.
- Zhou, B, Tarawmeh, M, Chu, D et al 2006, 'On a new quartet-based phylogeny reconstruction algorithm', International Conference on Bioinformatics & Computational Biology (BIOCOMP 2006), ed. Hamid R. Arabnia, Homayoun Valafar, CSREA Press, United States, pp. 87-93.
- Zhou, B, Tarawneh, M, Wang, C et al 2005, 'A novel quartet-based method for phylogenetic inference', IEEE Symposium on Bioinformatics and Bioengineering (BIBE 2005), ed. Conference Program Committee, IEEE Computer Society, New York, p. 2.
- Brent, R 2004, 'Brain drain: a more positive note', Australian Mathematical Society Gazette, vol. 31, no. 4, pp. 234-238.
- Brent, R 2004, 'Note on Marsaglia's xorshift random number generators', Journal of Statistical Software, vol. 11, no. 4, pp. 1-4.
- Brent, R, Larvala, S & Zimmermann, P 2004, 'A Primitive trinomial of degree 6972593', Mathematics of Computation, vol. 74, no. 250, pp. 1001-1002.
- Zhou, B & Brent, R 2003, 'An efficient method for computing eigenvalues of a real normal matrix', Journal of Parallel and Distributed Computing, vol. 63, pp. 638-648.
- Brent, R & Zimmermann, P 2003, 'Random number generators with period divisible by a Mersenne prime', International Conference on Computational Science and its Applications (ICCSA 2003), ed. Kumar, V.; Gavrilova, M.L.; Tan, C.J.K.; L'Ecuyer, P. (Eds.), Springer, Canada, pp. 1-10.
- Zhou, B, Goscinski, A & Brent, R 2003, 'Concerning the length of time slots for efficient gang scheduling', IEICE Transactions on Information and Systems, vol. E86-D, no. 9, pp. 1594-1600.
- Brent, R & Zimmermann, P 2003, 'Algorithms for finding almost irreducible and almost primitive trinomials', Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams, ed. Alf van der Poorten and Andreas Stein, American Mathematical Society, Toronto, Canada, pp. 91-102.
- Brent, R, Larvala, S & Zimmermann, P 2002, 'A fast algorithm for testing reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377', Mathematics of Computation, vol. 72, no. 243, pp. 1443-1452.
- Liang, W, Brent, R & Shen, H 2001, 'Fully dynamic maintenance of k-Connectivity in parallel', IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 8, pp. 846-864.
- Liang, W, Brent, R & Shen, H 2001, 'Fully Dynamic Maintenance of k-Connectivity in Parallel', IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 8, pp. 846-864.
- Zhou, B & Brent, R 1999, 'Job Repacking for Enhancing the Performance of Gang Scheduling', Lecture Notes in Computer Science (LNCS), vol. 1659, pp. 39-54.
Projects and Grants
Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.
- Robust numerical solution of partial differential equations on petascale computer systems with applications to tsunami modelling and plasma physics (Secondary Investigator)
- An Integrative and Interactive Approach for Co-estimation of Multiple Sequence Alignment and Phylogeny Reconstruction (Secondary Investigator)
- Integral lattices and their theta series (Secondary Investigator)
- Exploring the Frontiers of Feasible Computation (Primary Investigator)
- Centre for Statistical Modelling of Complex Systems (Primary Investigator)
