Richard P. Brent

Orcid: 0000-0002-8495-7437

Affiliations:
  • Australian National University, Acton, USA


According to our database1, Richard P. Brent authored at least 136 papers between 1971 and 2021.

Collaborative distances:

Awards

ACM Fellow

ACM Fellow 1995, "For research in the areas of parallel algorithms, computational number theory, multiple-precision arithmetic, computational complexity and numerical analysis, and leadership in Australian Computer Science.".

Timeline

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Bibliography

2021
Accurate estimation of sums over zeros of the Riemann zeta-function.
Math. Comput., 2021

Some Instructive Mathematical Errors.
Maple Trans., 2021

2019
A Conjectured Integer Sequence Arising From the Exponential Integral.
J. Integer Seq., 2019

2018
Computation of Maximal Determinants of Binary Circulant Matrices.
J. Integer Seq., 2018

2017
Reproducibility in Computational Science: A Case Study: Randomness of the Digits of Pi.
Exp. Math., 2017

2016
Some Binomial Sums Involving Absolute Values.
J. Integer Seq., 2016

Discrete analogues of Macdonald-Mehta integrals.
J. Comb. Theory A, 2016

Probabilistic lower bounds on maximal determinants of binary matrices.
Australas. J Comb., 2016

2015
A bound for the error term in the Brent-McMillan algorithm.
Math. Comput., 2015

Root optimization of polynomials in the number field sieve.
Math. Comput., 2015

Generalizing Tuenter's Binomial Sums.
J. Integer Seq., 2015

2013
Further analysis of the binary Euclidean algorithm
CoRR, 2013

General Lower Bounds on Maximal Determinants of Binary Matrices.
Electron. J. Comb., 2013

Finding D-optimal designs by randomised decomposition and switching.
Australas. J Comb., 2013

On the Sign of the Real Part of the Riemann Zeta Function.
Proceedings of the Number Theory and Related Fields, In Memory of Alf van der Poorten, 2013

2012
On the sign of the real part of the Riemann zeta-function
CoRR, 2012

2011
Finding many D-optimal designs by randomised decomposition and switching
CoRR, 2011

Fast computation of Bernoulli, Tangent and Secant numbers
CoRR, 2011

High-Performance Pseudo-Random Number Generation on Graphics Processing Units.
Proceedings of the Parallel Processing and Applied Mathematics, 2011

2010
The great trinomial hunt
CoRR, 2010

The myth of equidistribution for high-dimensional simulation
CoRR, 2010

A Simple Approach to Error Reconciliation in Quantum Key Distribution
CoRR, 2010

George Forsythe's last paper
CoRR, 2010

Note on Computing Ratings from Eigenvectors
CoRR, 2010

Stability of fast algorithms for structured linear systems
CoRR, 2010

Error analysis of a partial pivoting method for structured matrices
CoRR, 2010

A weakly stable algorithm for general Toeplitz systems
CoRR, 2010

Modern Computer Arithmetic (version 0.5.1)
CoRR, 2010

The complexity of multiple-precision arithmetic
CoRR, 2010

Multiple-precision zero-finding methods and the complexity of elementary function evaluation
CoRR, 2010

Some integer factorization algorithms using elliptic curves
CoRR, 2010

MP users guide
CoRR, 2010

Factorizations of Cunningham numbers with bases 13 to 99
CoRR, 2010

Some long-period random number generators using shifts and xors
CoRR, 2010

A fast vectorised implementation of Wallace's normal random number generator
CoRR, 2010

Uses of randomness in computation
CoRR, 2010

Fast normal random number generators on vector processors
CoRR, 2010

An O(M(n) log n) algorithm for the Jacobi symbol
CoRR, 2010

On computing factors of cyclotomic polynomials.
CoRR, 2010

On the periods of generalized Fibonacci recurrences.
CoRR, 2010

Parallel algorithms in linear algebra.
CoRR, 2010

An <i>O</i>(<i>M</i>(<i>n</i>) log<i>n</i>) Algorithm for the Jacobi Symbol.
Proceedings of the Algorithmic Number Theory, 9th International Symposium, 2010

2009
Minimum-energy all-to-all multicasting in wireless ad hoc networks.
IEEE Trans. Wirel. Commun., 2009

Ten new primitive binary trinomials.
Math. Comput., 2009

2008
Some Comments on C. S. Wallace's Random Number Generators.
Comput. J., 2008

On the Efficiency of Pollard's Rho Method for Discrete Logarithms.
Proceedings of the Theory of Computing 2008. Proc. Fourteenth Computing: The Australasian Theory Symposium (CATS 2008), 2008

Faster Multiplication in GF(2)[x].
Proceedings of the Algorithmic Number Theory, 8th International Symposium, 2008

2007
Error bounds on complex floating-point multiplication.
Math. Comput., 2007

A Multi-level Blocking Distinct Degree Factorization Algorithm
CoRR, 2007

A Global Maximum Likelihood Super-Quartet Phylogeny Method.
Proceedings of 5th Asia-Pacific Bioinformatics Conference, 2007

Extracting Significant Phrases from Text.
Proceedings of the 21st International Conference on Advanced Information Networking and Applications (AINA 2007), 2007

2006
Parallel implementation of a quartet-based algorithm for phylogenetic analysis.
Proceedings of the 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), 2006

On a New Quartet-Based Phylogeny Reconstruction Algorithm.
Proceedings of the 2006 International Conference on Bioinformatics & Computational Biology, 2006

Evidence of Multiple Maximum Likelihood Points for a Phylogenetic Tree.
Proceedings of the Sixth IEEE International Symposium on BioInformatics and BioEngineering (BIBE 2006), 2006

2005
A primitive trinomial of degree 6972593.
Math. Comput., 2005

A Novel Quartet-Based Method for Phylogenetic Inference.
Proceedings of the Fifth IEEE International Symposium on Bioinformatic and Bioengineering (BIBE 2005), 2005

2004
Parallel MCGLS and ICGLS Methods for Least Squares Problems on Distributed Memory Architectures.
J. Supercomput., 2004

Fast and Reliable Random Number Generators for Scientific Computing.
Proceedings of the Applied Parallel Computing, 2004

2003
Random Krylov Spaces over Finite Fields.
SIAM J. Discret. Math., 2003

A fast algorithm for testing reducibility of trinomials mod~2 and some new primitive trinomials of degree 3021377.
Math. Comput., 2003

An efficient method for computing eigenvalues of a real normal matrix.
J. Parallel Distributed Comput., 2003

The Improved Krylov Subspace Methods for Large and Sparse Linear Systems on Bulk Synchronous Parallel Architecture.
Proceedings of the 17th International Parallel and Distributed Processing Symposium (IPDPS 2003), 2003

Random Number Generators with Period Divisible by a Mersenne Prime.
Proceedings of the Computational Science and Its Applications, 2003

2002
The Improved BiCG Method for Large and Sparse Linear Systems on Parallel Distributed Memory Architectures.
Proceedings of the 16th International Parallel and Distributed Processing Symposium (IPDPS 2002), 2002

2001
Fully Dynamic Maintenance of k-Connectivity in Parallel.
IEEE Trans. Parallel Distributed Syst., 2001

On the Development of an Efficient Coscheduling System.
Proceedings of the Job Scheduling Strategies for Parallel Processing, 2001

Gang Scheduling with a Queue for Large Jobs.
Proceedings of the 15th International Parallel & Distributed Processing Symposium (IPDPS-01), 2001

The Improved Conjugate Gradient Squared (ICGS) Method on Parallel Distributed Memory Architectures.
Proceedings of the 30th International Workshops on Parallel Processing (ICPP 2001 Workshops), 2001

The Parallel Improved Lanczos Method for Integer Factorization over Finite Fields for Public Key Cryptosystems.
Proceedings of the 30th International Workshops on Parallel Processing (ICPP 2001 Workshops), 2001

2000
Adaptive AT2 optimal algorithms on reconfigurable meshes.
Parallel Comput., 2000

Three new factors of Fermat numbers.
Math. Comput., 2000

Resource Allocation Schemes for Gang Scheduling.
Proceedings of the Job Scheduling Strategies for Parallel Processing, IPDPS 2000 Workshop, 2000

Recent Progress and Prospects for Integer Factorisation Algorithms.
Proceedings of the Computing and Combinatorics, 6th Annual International Conference, 2000

How promising is the k-constrained reconfigurable mesh?
Proceedings of the ISCA 15th International Conference Computers and Their Applications, 2000

1999
Factorization of the tenth Fermat number.
Math. Comput., 1999

Maximal Contour Algorithms on Constrained Reconfigurable Meshes.
Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, 1999

An Efficient Resource Allocation Scheme for Gang Scheduling.
Proceedings of the International Workshop on Cluster Computing (IWCC '99), 1999

Job Re-pacing for Enhancing the Performance of Gang Scheduling.
Proceedings of the Job Scheduling Strategies for Parallel Processing, 1999

Some Parallel Algorithms for Integer Factorisation.
Proceedings of the Euro-Par '99 Parallel Processing, 5th International Euro-Par Conference, Toulouse, France, August 31, 1999

Computer Arithmetic - A Programmer's Perspective.
Proceedings of the 14th IEEE Symposium on Computer Arithmetic (Arith-14 '99), 1999

1998
Constant Time Algorithms for Computing the Contour of Maximal Elements on a Reconfigurable Mesh.
Parallel Process. Lett., 1998

Effective scheduling in a mixed parallel and sequential computing environment.
Proceedings of the Sixth Euromicro Workshop on Parallel and Distributed Processing, 1998

Job Scheduling Strategies for Networks of Workstations.
Proceedings of the Job Scheduling Strategies for Parallel Processing, 1998

Development of a Mathematical Subroutine Library for Fujitsu Vector Parallel Processors.
Proceedings of the 12th international conference on Supercomputing, 1998

Random Number Generation and Simulation on Vector and Parallel Computers.
Proceedings of the Euro-Par '98 Parallel Processing, 1998

On Quadratic Polynomials for the Number Field Sieve.
Proceedings of Computing: The Fourth Australasian Theory Symposium (CATS'98), 1998

1997
A Parallel Ring Ordering Algorithm for Efficient One-Sided Jacobi SVD Computations.
J. Parallel Distributed Comput., 1997

1996
Programming with transactions and chemical abstract machine.
Proceedings of the 1996 International Symposium on Parallel Architectures, 1996

Jacobi-like Algorithms for Eigenvalue Decomposition of a Real Normal Matrix Using Real Arithmetic.
Proceedings of IPPS '96, 1996

Constructing the Spanners of Graphs in Parallel.
Proceedings of IPPS '96, 1996

A Novel Parallel Algorithm for Enumerating Combinations.
Proceedings of the 1996 International Conference on Parallel Processing, 1996

A Comparative Study of Algorithms for Computing Continued Fractions of Algebraic Numbers.
Proceedings of the Algorithmic Number Theory, Second International Symposium, 1996

1995
On the Stability of the Bareiss and Related Toeplitz Factorization Algorithms.
SIAM J. Matrix Anal. Appl., 1995

Stability analysis of a general toeplitz systems solver.
Numer. Algorithms, 1995

A General-Purpose Parallel Sorting Algorithm.
Int. J. High Speed Comput., 1995

On parallel implementation of the one-sided Jacobi algorithm for singular value decompositions.
Proceedings of the 3rd Euromicro Workshop on Parallel and Distributed Processing (PDP '95), 1995

1994
Efficient Implementation of Sorting Algorithms on Asynchronous Distributed-Memory Machines.
Proceedings of the Proceedings 1994 International Conference on Parallel and Distributed Systems, 1994

Parallel and Distributed Processing Research in Some Asian Countries.
Proceedings of the Proceedings 1994 International Conference on Parallel and Distributed Systems, 1994

1993
Parallel Computation of the Singular Value Decomposition on Tree Architectures.
Proceedings of the 1993 International Conference on Parallel Processing, 1993

A fast, storage-efficient parallel sorting algorithm.
Proceedings of the International Conference on Application-Specific Array Processors, 1993

1992
Algorithmic Fault Tolerance Using the Lanczos Method.
SIAM J. Matrix Anal. Appl., 1992

1991
Fast training algorithms for multilayer neural nets.
IEEE Trans. Neural Networks, 1991

A Stabilized Parallel Algorithm for Direct-Form Recursive Filters.
IEEE Trans. Computers, 1991

1990
Linearly Connected Arrays for Toeplitz Least-Squares Problems.
J. Parallel Distributed Comput., 1990

1989
Efficient Implementation of the First-Fit Strategy for Dynamic Storage Allocation.
ACM Trans. Program. Lang. Syst., 1989

1988
A high throughput systolic implementation of the second order recursive filter.
Proceedings of the IEEE International Conference on Acoustics, 1988

1987
Determinants and ranks of random matrices over Z<sub>m</sub>.
Discret. Math., 1987

A Linear Algorithm for Data Compression.
Aust. Comput. J., 1987

1985
Tridiagonalization of a symmetric matrix on a square array of mesh-connected processors.
J. Parallel Distributed Comput., 1985

A systolic algorithm for integer GCD computation.
Proceedings of the 7th IEEE Symposium on Computer Arithmetic, 1985

1984
Systolic VLSI Arrays for Polynomial GCD Computation.
IEEE Trans. Computers, 1984

1983
Some Linear-Time Algorithms for Systolic Arrays.
Proceedings of the Information Processing 83, 1983

1982
A Regular Layout for Parallel Adders.
IEEE Trans. Computers, 1982

Some Area-Time Tradeoffs for VLSI.
SIAM J. Comput., 1982

Corrigendum: "The Area-Time Complexity of Binary Multiplication".
J. ACM, 1982

1981
The Area-Time Complexity of Binary Multiplication.
J. ACM, 1981

1980
An AUGMENT Interface for Brent's Multiple Precision Arithmetic Package.
ACM Trans. Math. Softw., 1980

On the Complexity of Composition and Generalized Composition of Power Series.
SIAM J. Comput., 1980

Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants.
J. Algorithms, 1980

On the Area of Binary Tree Layouts.
Inf. Process. Lett., 1980

Parallel Execution of a Sequence of tasks on a Asynchronous Multiprocessor.
Aust. Comput. J., 1980

The Chip Complexity of Binary Arithmetic
Proceedings of the 12th Annual ACM Symposium on Theory of Computing, 1980

Unrestricted Algorithms for Elementary and Special Functions.
Proceedings of the Information Processing, Proceedings of the 8th IFIP Congress 1980, Tokyo, Japan - October 6-9, 1980 and Melbourne, Australia, 1980

1979
Remark on "Algorithm 524: MP, A Fortran Multiple-Precision Arithmetic Package [A1]".
ACM Trans. Math. Softw., 1979

1978
Algorithm 524: MP, A Fortran Multiple-Precision Arithmetic Package [A1].
ACM Trans. Math. Softw., 1978

A Fortran Multiple-Precision Arithmetic Package.
ACM Trans. Math. Softw., 1978

Fast Algorithms for Manipulating Formal Power Series.
J. ACM, 1978

1976
Fast Multiple-Precision Evaluation of Elementary Functions.
J. ACM, 1976

Analysis of the binary Euclidean algorithm.
SIGSAM Bull., 1976

1974
The Parallel Evaluation of General Arithmetic Expressions.
J. ACM, 1974

A Gaussian Pseudo-Random Number Generator (Algorithm 488).
Commun. ACM, 1974

1973
On the Precision Attainable with Various Floating-Point Number Systems.
IEEE Trans. Computers, 1973

Reducing the Retrieval Time of Scatter Storage Techniques.
Commun. ACM, 1973

1972
The Computational Complexity of Iterative Methods for Systems of Nonlinear Equations.
Proceedings of a symposium on the Complexity of Computer Computations, 1972

1971
Algorithms for finding zeros and extrema of functions without calculating derivatives.
PhD thesis, 1971

An Algorithm with Guaranteed Convergence for Finding a Zero of a Function.
Comput. J., 1971


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