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Brent, Richard Peirce

Author ID: brent.richard-peirce Recent zbMATH articles by "Brent, Richard Peirce"
Published as: Brent, Richard P.; Brent, R. P.; Brent, Richard; Brent, Richard Peirce
External Links: MGP · ORCID · Wikidata · Twitter · dblp · GND · IdRef · theses.fr
all top 5

Co-Authors

55 single-authored
13 Zimmermann, Paul
11 Osborn, Judy-Anne H.
10 Kung, H. T.
7 Bojanczyk, Adam W.
5 Luk, Franklin T.
5 van de Lune, Jan
4 de Hoog, Frank Robert
4 Smith, Warren D.
4 te Riele, Herman
4 Yang, Laurence Tianruo
4 Zhou, Bing Bing
3 Abbott, James P.
3 Platt, David John
3 Trudgian, Timothy S.
2 Arias-de-Reyna, Juan
2 Bailey, David Harold
2 Cohen, Graeme L.
2 Larvala, Samuli
2 McKay, Brendan D.
2 Thomé, Emmanuel
2 Winter, Dik T.
1 Anderssen, Robert Scott
1 Angluin, Dana
1 Bai, Shi
1 Baudet, Gerard M.
1 Bloniarz, Peter A.
1 Boley, Daniel L.
1 Borodin, Allan B.
1 Borwein, Jonathan Michael
1 Borwein, Naomi Simone
1 Brown, Donna J.
1 Burachik, Regina Sandra
1 Carlson, David A.
1 Chazelle, Bernard
1 Cook, Stephen Arthur
1 Coons, Michael
1 Crandall, Richard E.
1 Cypher, A.
1 Daley, Daryl John
1 DeMillo, Richard Allan
1 Dilcher, Karl
1 Dobkin, David P.
1 Ehrig, Hartmut
1 Fagin, Ronald
1 Filotti, I. S.
1 Fischer, Michael J.
1 Frederickson, Greg N.
1 Gao, Shuhong
1 Gaudry, Pierrick
1 Glasser, M. Lawrence
1 Goldschlager, Leslie M.
1 Golub, Gene Howard
1 Guibas, Leonidas John
1 Gustavson, Fred G.
1 Guttmann, Anthony John
1 Harvey, David
1 Heintz, Joos
1 Hoffmann, Christoph M.
1 Hong, Jiawei
1 Hooper, Judith A.
1 Ibarra, Oscar H.
1 Ja’Ja’, Joseph F.
1 Johansson, Fredrik
1 Johnson, Donald B.
1 Joseph, Deborah
1 Kannan, Ravindran
1 Karp, Richard Manning
1 Krattenthaler, Christian Friedrich
1 Kruppa, Alexander
1 Kuck, David J.
1 Lauder, Alan G. B.
1 Leininger, Brian S.
1 Lichtenstein, David
1 Lipton, Richard Jay
1 Lloyd, Errol L.
1 Lynch, Nancy Ann
1 Mahr, Bernd
1 Maruyama, Kiyoshi
1 Mayer, Jack N.
1 McMillan, Edwin M.
1 Meyer, Albert Ronald
1 Miller, Gary Lee
1 Miller, Raymond E.
1 Mirkowska, Grazyna
1 Moran, Patrick Alfred Pierce
1 Murray, Lawrence M.
1 Murshed, M. Manzur
1 Nandapalan, Nimalan
1 Ohtsuka, Hideyuki
1 Orrick, William P.
1 Overmars, Mark H.
1 Parikh, Rohit
1 Paterson, Mike S.
1 Paul, Wolfgang Jakob
1 Percival, Colin
1 Pippenger, Nicholas J.
1 Plaisted, David Alan
1 Pollard, John M.
1 Pomerance, Carl Bernard
1 Pratt, Vaughan R.
...and 40 more Co-Authors
all top 5

Serials

23 Mathematics of Computation
6 IEEE Transactions on Computers
5 Journal of the Association for Computing Machinery
5 Journal of Integer Sequences
4 Journal of the Australian Mathematical Society, Series B
3 Numerische Mathematik
3 SIAM Journal on Scientific and Statistical Computing
2 Australian Computer Journal
2 Bulletin of the Australian Mathematical Society
2 SIAM Journal on Computing
2 SIAM Journal on Numerical Analysis
2 Journal of VLSI and Computer Systems
2 SIAM Journal on Matrix Analysis and Applications
2 Journal of Parallel and Distributed Computing
2 Communications of the ACM
2 Linear Algebra and its Applications
2 The Australasian Journal of Combinatorics
1 Computers & Mathematics with Applications
1 Discrete Mathematics
1 ACM Transactions on Mathematical Software
1 Ars Combinatoria
1 The Australian Mathematical Society Gazette
1 The Computer Journal. Section A / Section B
1 Journal of Combinatorial Theory. Series A
1 Journal of Number Theory
1 Journal of Algorithms
1 Parallel Computing
1 SIAM Journal on Discrete Mathematics
1 IMRN. International Mathematics Research Notices
1 The Journal of Supercomputing
1 Numerical Algorithms
1 IBM Journal of Research and Development
1 SIAM Journal on Applied Mathematics
1 Notices of the American Mathematical Society
1 Advances in Engineering Software
1 Experimental Mathematics
1 The Electronic Journal of Combinatorics
1 Integers
1 The ANZIAM Journal
1 Journal of the Australian Mathematical Society
1 Information
1 BIT. Nordisk Tidskrift for Informationsbehandling
1 Cambridge Monographs on Applied and Computational Mathematics
1 Springer Proceedings in Mathematics & Statistics

Publications by Year

Citations contained in zbMATH Open

107 Publications have been cited 1,751 times in 1,583 Documents Cited by Year
Algorithms for minimization without derivatives. Zbl 0245.65032
Brent, Richard P.
380
1973
The parallel evaluation of general arithmetic expressions. Zbl 0276.68010
Brent, Richard P.
146
1974
Fast solution of Toeplitz systems of equations and computation of Padé approximants. Zbl 0475.65018
Brent, Richard P.; Gustavson, Fred G.; Yun, David Y. Y.
114
1980
Fast multiple-precision evaluation of elementary functions. Zbl 0324.65018
Brent, Richard P.
86
1976
Fast algorithms for manipulating formal power series. Zbl 0388.68052
Brent, R. P.; Kung, H. T.
85
1978
An algorithm with guaranteed convergence for finding a zero of a function. Zbl 0231.65046
Brent, R. P.
69
1971
Some efficient algorithms for solving systems of nonlinear equations. Zbl 0258.65051
Brent, Richard P.
58
1973
Modern computer arithmetic. Zbl 1230.68014
Brent, Richard; Zimmermann, Paul
52
2011
An improved Monte Carlo factorization algorithm. Zbl 0439.65001
Brent, Richard P.
38
1980
Algorithms for minimization without derivatives. Repr. of the 1973 original. Zbl 1009.90133
Brent, Richard P.
37
2002
The solution of singular-value and symmetric eigenvalue problems on multiprocessor arrays. Zbl 0575.65027
Brent, Richard P.; Luk, Franklin T.
31
1985
The area-time complexity of binary multiplication. Zbl 0462.68014
Brent, R. P.; Kung, H. T.
30
1981
Error analysis of algorithms for matrix multiplication and triangular decomposition using Winograd’s identity. Zbl 0193.11902
Brent, R. P.
25
1970
Computation of the singular value decomposition using mesh-connected processors. Zbl 0597.65029
Brent, Richard P.; Luk, Franklin T.; Van Loan, Charles F.
22
1985
A note on downdating the Cholesky factorization. Zbl 0617.65013
Bojanczyk, A. W.; Brent, R. P.; van Dooren, P.; de Hoog, F. R.
22
1987
Improved techniques for lower bounds for odd perfect numbers. Zbl 0736.11004
Brent, R. P.; Cohen, G. L.; te Riele, Herman J. J.
20
1991
Solving triangular systems on a parallel computer. Zbl 0375.65016
Sameh, Ahmed H.; Brent, Richard P.
20
1977
A regular layout for parallel adders. Zbl 0477.94037
Brent, Richard P.; Kung, H. T.
20
1982
On the zeros of the Riemann zeta function in the critical strip. Zbl 0422.10031
Brent, Richard P.
19
1979
Factorization of the eighth Fermat number. Zbl 0476.10007
Brent, Richard P.; Pollard, John M.
17
1981
On the stability of the Bareiss and related Toeplitz factorization algorithms. Zbl 0819.65016
Bojanczyk, A. W.; Brent, R. P.; De Hoog, F. R.; Sweet, D. R.
16
1995
QR factorization of Toeplitz matrices. Zbl 0574.65019
Bojanczyk, A. W.; Brent, R. P.; de Hoog, F. R.
16
1986
The first occurrence of large gaps between successive primes. Zbl 0269.10002
Brent, Richard P.
15
1973
Reducing the retrieval time of scatter storage techniques. Zbl 0251.68019
Brent, Richard P.
13
1973
Determinants and ranks of random matrices over \({\mathbb{Z}}_ m\). Zbl 0628.15010
Brent, Richard P.; McKay, Brendan D.
13
1987
On the zeros of the Riemann zeta function in the critical strip. II. Zbl 0486.10028
Brent, R. P.; van de Lune, J.; te Riele, Herman J. J.; Winter, D. T.
13
1982
The parallel evaluation of arithmetic expression without division. Zbl 0252.68028
Brent, Richard; Kuck, David; Maruyama, Kiyoshi
12
1973
Error bounds on complex floating-point multiplication. Zbl 1118.65031
Brent, Richard; Percival, Colin; Zimmermann, Paul
12
2007
Some new algorithms for high-precision computation of Euler’s constant. Zbl 0442.10002
Brent, Richard P.; McMillan, Edwin M.
12
1980
Recent progress and prospects for integer factorisation algorithms. Zbl 0988.11056
Brent, Richard P.
11
2000
Optimal iterative processes for root-finding. Zbl 0252.65041
Brent, Richard; Winograd, Shmuel; Wolfe, Philip
11
1973
A new algorithm for minimizing a function of several variables without calculating derivatives. Zbl 0311.90065
Brent, R. P.
10
1972
Fast computation of Bernoulli, tangent and secant numbers. Zbl 1310.11120
Brent, Richard P.; Harvey, David
10
2013
On the periods of generalized Fibonacci recurrences. Zbl 0809.11083
Brent, Richard P.
9
1994
A Gaussian pseudo-random number generator \([G5]\). Zbl 0292.65003
Brent, Richard P.
9
1974
Irregularities in the distribution of primes and twin primes. Zbl 0295.10002
Brent, Richard P.
9
1975
Concerning \(\int^1_0\dots\int^1_0(\chi^2_1+\dots+\chi^2_k)^{1/2}d\chi_1\dots d\chi_k\) and a Taylor series method. Zbl 0337.65022
Anderssen, R. S.; Brent, R. P.; Daley, D. J.; Moran, P. A. P.
9
1976
Numerically stable solution of dense systems of linear equations using mesh-connected processors. Zbl 0574.65020
Bojanczyk, A.; Brent, R. P.; Kung, H. T.
8
1984
On computing factors of cyclotomic polynomials. Zbl 0785.11011
Brent, Richard P.
8
1993
On the Davidenko-Branin method for solving simultaneous nonlinear equations. Zbl 0276.65023
Brent, R. P.
8
1972
Faster multiplication in \(\text{GF}(2)[x]\). Zbl 1230.11152
Brent, Richard P.; Gaudry, Pierrick; Thomé, Emmanuel; Zimmermann, Paul
8
2008
Multiple-precision zero-finding methods and the complexity of elementary function evaluation. Zbl 0342.65031
Brent, Richard P.
8
1976
Accurate estimation of sums over zeros of the Riemann zeta-function. Zbl 1480.11103
Brent, Richard P.; Platt, David J.; Trudgian, Timothy S.
8
2021
Algebraic independence of Mahler functions via radial asymptotics. Zbl 1415.11104
Brent, Richard P.; Coons, Michael; Zudilin, Wadim
8
2016
The improved parallel BiCG method for large and sparse unsymmetric linear systems on distributed memory architectures. Zbl 1103.65342
Yang, Laurence Tianruo; Brent, Richard P.
7
2003
On the addition of binary numbers. Zbl 0199.51702
Brent, R.
7
1970
Discrete analogues of Macdonald-Mehta integrals. Zbl 1343.05160
Brent, Richard P.; Krattenthaler, Christian; Warnaar, Ole
7
2016
The great trinomial hunt. Zbl 1277.11110
Brent, Richard P.; Zimmermann, Paul
7
2011
Fast local convergence with single and multistep methods for nonlinear equations. Zbl 0359.65044
Abbott, James P.; Brent, Richard P.
7
1975
A systolic array for the linear-time solution of Toeplitz systems of equations. Zbl 0532.68049
Brent, Richard P.; Luk, Franklin T.
6
1983
Random Krylov spaces over finite fields. Zbl 1044.11104
Brent, Richard P.; Gao, Shuhong; Lauder, Alan G. B.
6
2003
Systolic VLSI arrays for polynomial GCD computation. Zbl 0542.94043
Brent, Richard P.; Kung, H. T.
6
1984
Some binomial sums involving absolute values. Zbl 1336.05006
Brent, Richard P.; Ohtsuka, Hideyuki; Osborn, Judy-Anne H.; Prodinger, Helmut
6
2016
A linear algorithm for data compression. Zbl 0641.68029
Brent, R. P.
6
1987
Root optimization of polynomials in the number field sieve. Zbl 1378.11104
Bai, Shi; Brent, Richard P.; Thomé, Emmanuel
6
2015
Note on best possible bounds for determinants of matrices close to the identity matrix. Zbl 1303.15007
Brent, Richard P.; Osborn, Judy-anne H.; Smith, Warren D.
6
2015
General lower bounds on maximal determinants of binary matrices. Zbl 1267.05052
Brent, Richard P.; Osborn, Judy-Anne H.
6
2013
A comparative study of algorithms for computing continued fractions of algebraic numbers. Zbl 0899.11065
Brent, Richard P.; te Riele, Herman J. J.; van der Poorten, Alfred J.
5
1996
A fast algorithm for testing reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377. Zbl 1119.11320
Brent, Richard P.; Larvala, Samuli; Zimmermann, Paul
5
2003
Some long-period random number generators using shifts and xors. Zbl 1334.65012
Brent, Richard Peirce
5
2007
Factorization of the tenth Fermat number. Zbl 0977.11053
Brent, Richard P.
5
1999
Ten new primitive binary trinomials. Zbl 1206.11010
Brent, Richard P.; Zimmermann, Paul
5
2009
Unrestricted algorithms for elementary and special functions. Zbl 0442.65013
Brent, Richard P.
5
1980
The first occurrence of certain large prime gaps. Zbl 0443.10003
Brent, Richard P.
5
1980
On determinants of random symmetric matrices over \(Z_ m\). Zbl 0691.15010
Brent, Richard P.; McKay, Brendan D.
5
1988
Algorithmic fault tolerance using the Lanczos method. Zbl 0760.65048
Boley, Daniel L.; Brent, Richard P.; Golub, Gene H.; Luk, Franklin T.
4
1992
A parallel ring ordering algorithm for efficient one-sided Jacobi SVD computations. Zbl 0880.68055
Zhou, B. B.; Brent, R. P.
4
1997
Algorithms for finding almost irreducible and almost primitive trinomials. Zbl 1087.11075
Brent, Richard P.; Zimmermann, Paul
4
2004
The distribution of small gaps between successive primes. Zbl 0274.10001
Brent, Richard P.
4
1974
Fast algorithms for composition and reversion of multivariate power series (preliminary version). Zbl 0411.68043
Brent, R. P.; Kung, H. T.
4
1977
On the complexity of composition and generalized composition of power series. Zbl 0447.68033
Brent, R. P.; Traub, J. F.
4
1980
A new lower bound for odd perfect numbers. Zbl 0672.10006
Brent, Richard P.; Cohen, Graeme L.
4
1989
Probabilistic lower bounds on maximal determinants of binary matrices. Zbl 1375.05042
Brent, Richard P.; Osborn, Judy-Anne H.; Smith, Warren D.
3
2016
On the precision attainable with various floating-point number systems. Zbl 0261.65036
Brent, Richard P.
3
1973
A bound for the error term in the Brent-McMillan algorithm. Zbl 1320.33007
Brent, Richard P.; Johansson, Fredrik
3
2015
A multi-level blocking distinct-degree factorization algorithm. Zbl 1213.11199
Brent, Richard P.; Zimmermann, Paul
3
2008
Computation of the regular continued fraction for Euler’s constant. Zbl 0369.10002
Brent, Richard P.
3
1977
Reproducibility in computational science: A case study: randomness of the digits of pi. Zbl 1426.11133
Bailey, David H.; Borwein, Jonathan M.; Brent, Richard P.; Reisi, Mohsen
3
2017
The mean square of the error term in the prime number theorem. Zbl 1508.11094
Brent, Richard P.; Platt, David J.; Trudgian, Timothy S.
3
2022
On quadratic polynomials for the number field sieve. Repr. from Australian Computer Science Communications 20, No. 3 (1998). Zbl 0990.11080
Murphy, Brian; Brent, Richard P.
2
1998
On the accuracy of asymptotic approximations to the log-gamma and Riemann-Siegel theta functions. Zbl 1436.11106
Brent, Richard P.
2
2019
Parallel algorithms for Toeplitz systems. Zbl 0735.65009
Brent, Richard P.
2
1991
Stability analysis of a general Toeplitz system solver. Zbl 0837.65017
Bojanczyk, Adam W.; Brent, Richard P.; de Hoog, Frank R.
2
1995
The parallel evaluation of arithmetic expressions in logarithmic time. Zbl 0273.68037
Brent, Richard P.
2
1973
An efficient method for computing eigenvalues of a real normal matrix. Zbl 1056.65032
Zhou, B. B.; Brent, R. P.
2
2003
Parallel algorithms for integer factorisation. Zbl 0709.11074
Brent, Richard P.
2
1990
Finding D-optimal designs by randomised decomposition and switching. Zbl 1278.05059
Brent, Richard P.
2
2013
On minors of maximal determinant matrices. Zbl 1310.15055
Brent, Richard P.; Osborn, Judy-Anne H.
2
2013
Analysis of the binary Euclidean algorithm. Zbl 0373.68040
Brent, Richard P.
2
1976
Succinct proofs of primality for the factors of some Fermat numbers. Zbl 0478.10005
Brent, Richard P.
2
1982
Parallel algorithms for digital signal processing. Zbl 0736.65012
Brent, Richard P.
1
1991
Computing Aurifeuillian factors. Zbl 0840.12003
Brent, Richard P.
1
1995
Random number generation and simulation on vector and parallel computers. Zbl 0928.65010
Brent, Richard P.
1
1998
A primitive trinomial of degree 6972593. Zbl 1077.11002
Brent, Richard P.; Larvala, Samuli; Zimmermann, Paul
1
2005
A conjectured integer sequence arising from the exponential integral. Zbl 1431.30003
Brent, Richard P.; Glasser, M. L.; Guttmann, Anthony J.
1
2019
Computation of maximal determinants of binary circulant matrices. Zbl 1388.05028
Brent, Richard P.; Yedidia, Adam B.
1
2018
Three new factors of Fermat numbers. Zbl 1042.11082
Brent, R. P.; Crandall, R. E.; Dilcher, K.; Van Halewyn, C.
1
2000
Some high-order zero-finding methods using almost orthogonal polynomials. Zbl 0333.65022
Brent, Richard P.
1
1975
Generalizing Tuenter’s binomial sums. Zbl 1309.05013
Brent, Richard P.
1
2015
Parallel solution of certain Toeplitz least-squares problems. Zbl 0587.65031
Bojańczyk, A.; Brent, R. P.
1
1986
The mean square of the error term in the prime number theorem. Zbl 1508.11094
Brent, Richard P.; Platt, David J.; Trudgian, Timothy S.
3
2022
Accurate estimation of sums over zeros of the Riemann zeta-function. Zbl 1480.11103
Brent, Richard P.; Platt, David J.; Trudgian, Timothy S.
8
2021
A harmonic sum over nontrivial zeros of the Riemann zeta-function. Zbl 1479.11144
Brent, Richard P.; Platt, David J.; Trudgian, Timothy S.
1
2021
On the accuracy of asymptotic approximations to the log-gamma and Riemann-Siegel theta functions. Zbl 1436.11106
Brent, Richard P.
2
2019
A conjectured integer sequence arising from the exponential integral. Zbl 1431.30003
Brent, Richard P.; Glasser, M. L.; Guttmann, Anthony J.
1
2019
Computation of maximal determinants of binary circulant matrices. Zbl 1388.05028
Brent, Richard P.; Yedidia, Adam B.
1
2018
Reproducibility in computational science: A case study: randomness of the digits of pi. Zbl 1426.11133
Bailey, David H.; Borwein, Jonathan M.; Brent, Richard P.; Reisi, Mohsen
3
2017
Algebraic independence of Mahler functions via radial asymptotics. Zbl 1415.11104
Brent, Richard P.; Coons, Michael; Zudilin, Wadim
8
2016
Discrete analogues of Macdonald-Mehta integrals. Zbl 1343.05160
Brent, Richard P.; Krattenthaler, Christian; Warnaar, Ole
7
2016
Some binomial sums involving absolute values. Zbl 1336.05006
Brent, Richard P.; Ohtsuka, Hideyuki; Osborn, Judy-Anne H.; Prodinger, Helmut
6
2016
Probabilistic lower bounds on maximal determinants of binary matrices. Zbl 1375.05042
Brent, Richard P.; Osborn, Judy-Anne H.; Smith, Warren D.
3
2016
Root optimization of polynomials in the number field sieve. Zbl 1378.11104
Bai, Shi; Brent, Richard P.; Thomé, Emmanuel
6
2015
Note on best possible bounds for determinants of matrices close to the identity matrix. Zbl 1303.15007
Brent, Richard P.; Osborn, Judy-anne H.; Smith, Warren D.
6
2015
A bound for the error term in the Brent-McMillan algorithm. Zbl 1320.33007
Brent, Richard P.; Johansson, Fredrik
3
2015
Generalizing Tuenter’s binomial sums. Zbl 1309.05013
Brent, Richard P.
1
2015
Fast computation of Bernoulli, tangent and secant numbers. Zbl 1310.11120
Brent, Richard P.; Harvey, David
10
2013
General lower bounds on maximal determinants of binary matrices. Zbl 1267.05052
Brent, Richard P.; Osborn, Judy-Anne H.
6
2013
Finding D-optimal designs by randomised decomposition and switching. Zbl 1278.05059
Brent, Richard P.
2
2013
On minors of maximal determinant matrices. Zbl 1310.15055
Brent, Richard P.; Osborn, Judy-Anne H.
2
2013
Modern computer arithmetic. Zbl 1230.68014
Brent, Richard; Zimmermann, Paul
52
2011
The great trinomial hunt. Zbl 1277.11110
Brent, Richard P.; Zimmermann, Paul
7
2011
An \(O(M(n) \log n)\) algorithm for the Jacobi symbol. Zbl 1260.11081
Brent, Richard P.; Zimmermann, Paul
1
2010
Ten new primitive binary trinomials. Zbl 1206.11010
Brent, Richard P.; Zimmermann, Paul
5
2009
Faster multiplication in \(\text{GF}(2)[x]\). Zbl 1230.11152
Brent, Richard P.; Gaudry, Pierrick; Thomé, Emmanuel; Zimmermann, Paul
8
2008
A multi-level blocking distinct-degree factorization algorithm. Zbl 1213.11199
Brent, Richard P.; Zimmermann, Paul
3
2008
Error bounds on complex floating-point multiplication. Zbl 1118.65031
Brent, Richard; Percival, Colin; Zimmermann, Paul
12
2007
Some long-period random number generators using shifts and xors. Zbl 1334.65012
Brent, Richard Peirce
5
2007
A primitive trinomial of degree 6972593. Zbl 1077.11002
Brent, Richard P.; Larvala, Samuli; Zimmermann, Paul
1
2005
Algorithms for finding almost irreducible and almost primitive trinomials. Zbl 1087.11075
Brent, Richard P.; Zimmermann, Paul
4
2004
The improved parallel BiCG method for large and sparse unsymmetric linear systems on distributed memory architectures. Zbl 1103.65342
Yang, Laurence Tianruo; Brent, Richard P.
7
2003
Random Krylov spaces over finite fields. Zbl 1044.11104
Brent, Richard P.; Gao, Shuhong; Lauder, Alan G. B.
6
2003
A fast algorithm for testing reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377. Zbl 1119.11320
Brent, Richard P.; Larvala, Samuli; Zimmermann, Paul
5
2003
An efficient method for computing eigenvalues of a real normal matrix. Zbl 1056.65032
Zhou, B. B.; Brent, R. P.
2
2003
Algorithms for minimization without derivatives. Repr. of the 1973 original. Zbl 1009.90133
Brent, Richard P.
37
2002
Recent progress and prospects for integer factorisation algorithms. Zbl 0988.11056
Brent, Richard P.
11
2000
Three new factors of Fermat numbers. Zbl 1042.11082
Brent, R. P.; Crandall, R. E.; Dilcher, K.; Van Halewyn, C.
1
2000
Factorization of the tenth Fermat number. Zbl 0977.11053
Brent, Richard P.
5
1999
On quadratic polynomials for the number field sieve. Repr. from Australian Computer Science Communications 20, No. 3 (1998). Zbl 0990.11080
Murphy, Brian; Brent, Richard P.
2
1998
Random number generation and simulation on vector and parallel computers. Zbl 0928.65010
Brent, Richard P.
1
1998
A parallel ring ordering algorithm for efficient one-sided Jacobi SVD computations. Zbl 0880.68055
Zhou, B. B.; Brent, R. P.
4
1997
A comparative study of algorithms for computing continued fractions of algebraic numbers. Zbl 0899.11065
Brent, Richard P.; te Riele, Herman J. J.; van der Poorten, Alfred J.
5
1996
On the stability of the Bareiss and related Toeplitz factorization algorithms. Zbl 0819.65016
Bojanczyk, A. W.; Brent, R. P.; De Hoog, F. R.; Sweet, D. R.
16
1995
Stability analysis of a general Toeplitz system solver. Zbl 0837.65017
Bojanczyk, Adam W.; Brent, Richard P.; de Hoog, Frank R.
2
1995
Computing Aurifeuillian factors. Zbl 0840.12003
Brent, Richard P.
1
1995
On the periods of generalized Fibonacci recurrences. Zbl 0809.11083
Brent, Richard P.
9
1994
On computing factors of cyclotomic polynomials. Zbl 0785.11011
Brent, Richard P.
8
1993
Algorithmic fault tolerance using the Lanczos method. Zbl 0760.65048
Boley, Daniel L.; Brent, Richard P.; Golub, Gene H.; Luk, Franklin T.
4
1992
Improved techniques for lower bounds for odd perfect numbers. Zbl 0736.11004
Brent, R. P.; Cohen, G. L.; te Riele, Herman J. J.
20
1991
Parallel algorithms for Toeplitz systems. Zbl 0735.65009
Brent, Richard P.
2
1991
Parallel algorithms for digital signal processing. Zbl 0736.65012
Brent, Richard P.
1
1991
Parallel algorithms for integer factorisation. Zbl 0709.11074
Brent, Richard P.
2
1990
A new lower bound for odd perfect numbers. Zbl 0672.10006
Brent, Richard P.; Cohen, Graeme L.
4
1989
On determinants of random symmetric matrices over \(Z_ m\). Zbl 0691.15010
Brent, Richard P.; McKay, Brendan D.
5
1988
A note on downdating the Cholesky factorization. Zbl 0617.65013
Bojanczyk, A. W.; Brent, R. P.; van Dooren, P.; de Hoog, F. R.
22
1987
Determinants and ranks of random matrices over \({\mathbb{Z}}_ m\). Zbl 0628.15010
Brent, Richard P.; McKay, Brendan D.
13
1987
A linear algorithm for data compression. Zbl 0641.68029
Brent, R. P.
6
1987
A systolic algorithm for extended GCD computation. Zbl 0657.10002
Bojanczyk, A. W.; Brent, R. P.
1
1987
QR factorization of Toeplitz matrices. Zbl 0574.65019
Bojanczyk, A. W.; Brent, R. P.; de Hoog, F. R.
16
1986
Parallel solution of certain Toeplitz least-squares problems. Zbl 0587.65031
Bojańczyk, A.; Brent, R. P.
1
1986
The solution of singular-value and symmetric eigenvalue problems on multiprocessor arrays. Zbl 0575.65027
Brent, Richard P.; Luk, Franklin T.
31
1985
Computation of the singular value decomposition using mesh-connected processors. Zbl 0597.65029
Brent, Richard P.; Luk, Franklin T.; Van Loan, Charles F.
22
1985
Numerically stable solution of dense systems of linear equations using mesh-connected processors. Zbl 0574.65020
Bojanczyk, A.; Brent, R. P.; Kung, H. T.
8
1984
Systolic VLSI arrays for polynomial GCD computation. Zbl 0542.94043
Brent, Richard P.; Kung, H. T.
6
1984
A systolic array for the linear-time solution of Toeplitz systems of equations. Zbl 0532.68049
Brent, Richard P.; Luk, Franklin T.
6
1983
A regular layout for parallel adders. Zbl 0477.94037
Brent, Richard P.; Kung, H. T.
20
1982
On the zeros of the Riemann zeta function in the critical strip. II. Zbl 0486.10028
Brent, R. P.; van de Lune, J.; te Riele, Herman J. J.; Winter, D. T.
13
1982
Succinct proofs of primality for the factors of some Fermat numbers. Zbl 0478.10005
Brent, Richard P.
2
1982
Some area-time tradeoffs for VLSI. Zbl 0492.68041
Brent, Richard P.; Goldschlager, Leslie M.
1
1982
The first 200,000,001 zeros of Riemann’s zeta function. Zbl 0516.10031
Brent, R. P.; van de Lune, J.; te Riele, Herman J. J.; Winter, D. T.
1
1982
The area-time complexity of binary multiplication. Zbl 0462.68014
Brent, R. P.; Kung, H. T.
30
1981
Factorization of the eighth Fermat number. Zbl 0476.10007
Brent, Richard P.; Pollard, John M.
17
1981
Fast solution of Toeplitz systems of equations and computation of Padé approximants. Zbl 0475.65018
Brent, Richard P.; Gustavson, Fred G.; Yun, David Y. Y.
114
1980
An improved Monte Carlo factorization algorithm. Zbl 0439.65001
Brent, Richard P.
38
1980
Some new algorithms for high-precision computation of Euler’s constant. Zbl 0442.10002
Brent, Richard P.; McMillan, Edwin M.
12
1980
Unrestricted algorithms for elementary and special functions. Zbl 0442.65013
Brent, Richard P.
5
1980
The first occurrence of certain large prime gaps. Zbl 0443.10003
Brent, Richard P.
5
1980
On the complexity of composition and generalized composition of power series. Zbl 0447.68033
Brent, R. P.; Traub, J. F.
4
1980
An AUGMENT interface for Brent’s multiple precision arithmetic package. Zbl 0433.68028
Brent, Richard P.; Hooper, Judith A.; Yohe, J. Michael
1
1980
On the zeros of the Riemann zeta function in the critical strip. Zbl 0422.10031
Brent, Richard P.
19
1979
Fast algorithms for manipulating formal power series. Zbl 0388.68052
Brent, R. P.; Kung, H. T.
85
1978
Solving triangular systems on a parallel computer. Zbl 0375.65016
Sameh, Ahmed H.; Brent, Richard P.
20
1977
Fast algorithms for composition and reversion of multivariate power series (preliminary version). Zbl 0411.68043
Brent, R. P.; Kung, H. T.
4
1977
Computation of the regular continued fraction for Euler’s constant. Zbl 0369.10002
Brent, Richard P.
3
1977
Fast multiple-precision evaluation of elementary functions. Zbl 0324.65018
Brent, Richard P.
86
1976
Concerning \(\int^1_0\dots\int^1_0(\chi^2_1+\dots+\chi^2_k)^{1/2}d\chi_1\dots d\chi_k\) and a Taylor series method. Zbl 0337.65022
Anderssen, R. S.; Brent, R. P.; Daley, D. J.; Moran, P. A. P.
9
1976
Multiple-precision zero-finding methods and the complexity of elementary function evaluation. Zbl 0342.65031
Brent, Richard P.
8
1976
Analysis of the binary Euclidean algorithm. Zbl 0373.68040
Brent, Richard P.
2
1976
A class of optimal-order zero-finding methods using derivative evaluations. Zbl 0342.65030
Brent, Richard P.
1
1976
Irregularities in the distribution of primes and twin primes. Zbl 0295.10002
Brent, Richard P.
9
1975
Fast local convergence with single and multistep methods for nonlinear equations. Zbl 0359.65044
Abbott, James P.; Brent, Richard P.
7
1975
Some high-order zero-finding methods using almost orthogonal polynomials. Zbl 0333.65022
Brent, Richard P.
1
1975
The parallel evaluation of general arithmetic expressions. Zbl 0276.68010
Brent, Richard P.
146
1974
A Gaussian pseudo-random number generator \([G5]\). Zbl 0292.65003
Brent, Richard P.
9
1974
The distribution of small gaps between successive primes. Zbl 0274.10001
Brent, Richard P.
4
1974
Algorithms for minimization without derivatives. Zbl 0245.65032
Brent, Richard P.
380
1973
Some efficient algorithms for solving systems of nonlinear equations. Zbl 0258.65051
Brent, Richard P.
58
1973
The first occurrence of large gaps between successive primes. Zbl 0269.10002
Brent, Richard P.
15
1973
Reducing the retrieval time of scatter storage techniques. Zbl 0251.68019
Brent, Richard P.
13
1973
The parallel evaluation of arithmetic expression without division. Zbl 0252.68028
Brent, Richard; Kuck, David; Maruyama, Kiyoshi
12
1973
Optimal iterative processes for root-finding. Zbl 0252.65041
Brent, Richard; Winograd, Shmuel; Wolfe, Philip
11
1973
...and 7 more Documents
all top 5

Cited by 2,429 Authors

31 Brent, Richard Peirce
22 Pan, Victor Yakovlevich
19 Schost, Éric
18 van der Hoeven, Joris
11 Rump, Siegfried Michael
9 Bojanczyk, Adam W.
9 Harvey, David
8 de la Llave, Rafael
8 Panario, Daniel
8 Petković, Miodrag S.
7 Akl, Selim G.
7 Bach, Eric
7 Gu, Tongxiang
7 Jeannerod, Claude-Pierre
7 Lecerf, Grégoire
7 Zuo, Xianyu
6 Borwein, Jonathan Michael
6 Breslauer, Dany
6 Heinig, Georg
6 Johansson, Fredrik
6 Potra, Florian-Alexandru
6 Trudgian, Timothy S.
6 Van Dooren, Paul M.
6 von zur Gathen, Joachim
6 Zimmermann, Paul
5 Atallah, Mikhail J.
5 Borwein, Peter Benjamin
5 Bostan, Alin
5 Bravo, Jhon Jairo
5 Codenotti, Bruno
5 Cohen, Graeme L.
5 Crandall, Richard E.
5 Dvurechensky, Pavel E.
5 Džunić, Jovana
5 Falcone, Maurizio
5 Gasnikov, Aleksandr V.
5 Karatsuba, Ekaterina Anatol’evna
5 Limaye, Nutan
5 Mastronardi, Nicola
5 Mezzarobba, Marc
5 Muller, Jean-Michel
5 Preparata, Franco P.
5 Salvy, Bruno
5 Sharma, Janak Raj
5 Van Barel, Marc
5 Zhang, Litao
4 Agarwal, Ravi P.
4 Bailey, David Harold
4 Celletti, Alessandra
4 Chen, Danny Ziyi
4 Chen, Lin
4 Coons, Michael
4 Cully-Hugill, Michaela
4 Doliskani, Javad
4 Eppstein, David Arthur
4 Fortes, Miguel Angel
4 Galil, Zvi
4 Glowinski, Roland
4 Goodrich, Michael Truman
4 Hansen, Pierre
4 Jaumard, Brigitte
4 Johnston, Daniel R.
4 Kotsireas, Ilias S.
4 Kumar, Sunil
4 Luca, Florian
4 Mahajan, Meena
4 Owen, Art B.
4 Pasadas, Miguel
4 Petković, Ljiljana D.
4 Raghavendra Rao, B. V.
4 Samar, Mahvish
4 Sen, Syamal Kumar
4 Thomé, Emmanuel
4 Trench, William F.
4 Vrahatis, Michael N.
4 Yap, Chee-Keng
4 You, Xu
4 Zufiria, Pedro J.
3 Alefeld, Götz E.
3 Andrews, Jeffrey L.
3 Argyros, Ioannis Konstantinos
3 Barrio, Roberto
3 Bernstein, Daniel Julius
3 Berthomieu, Jérémy
3 Blakey, Ed
3 Büthe, Jan
3 Calleja, Renato C.
3 Cao, Xiaodong
3 Carlini, Elisabetta
3 Charlier, J.-P.
3 Chillara, Suryajith
3 De Agostino, Sergio
3 De Feo, Luca
3 Deng, Naiyang
3 Eldén, Lars
3 Farooq, Aamir
3 Farouki, Rida T.
3 Ferretti, Roberto Giorgio
3 Gao, Wei
3 Gaudry, Pierrick
...and 2,329 more Authors
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Cited in 393 Serials

102 Mathematics of Computation
74 Linear Algebra and its Applications
52 Journal of Computational and Applied Mathematics
44 Journal of Symbolic Computation
37 Computers & Mathematics with Applications
34 Applied Mathematics and Computation
34 Theoretical Computer Science
33 Information Processing Letters
33 Journal of Computational Physics
30 Numerische Mathematik
27 Journal of Complexity
25 Algorithmica
22 Computational Statistics and Data Analysis
21 BIT
21 Computing
17 Journal of Computer and System Sciences
17 Numerical Algorithms
17 International Journal of Computer Mathematics
15 Discrete Applied Mathematics
13 Computer Methods in Applied Mechanics and Engineering
11 Calcolo
11 Journal of Number Theory
11 Journal of Optimization Theory and Applications
11 European Journal of Operational Research
11 Journal of Statistical Computation and Simulation
10 Mathematics and Computers in Simulation
10 Mathematical Programming. Series A. Series B
10 SIAM Journal on Scientific Computing
10 Parallel Algorithms and Applications
9 Computer Physics Communications
9 Mathematical Programming
9 Information and Computation
9 Applicable Algebra in Engineering, Communication and Computing
8 Journal of Integer Sequences
7 Journal of Mathematical Analysis and Applications
7 The Mathematical Intelligencer
7 Applied Numerical Mathematics
7 Journal of Global Optimization
7 Communications in Statistics. Simulation and Computation
7 Finite Fields and their Applications
7 The Ramanujan Journal
7 Optimization Methods & Software
6 Computers and Fluids
6 Psychometrika
6 Information Sciences
6 Computational Geometry
6 Computational Complexity
6 Experimental Mathematics
5 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
5 Automatica
5 Journal of Econometrics
5 SIAM Journal on Computing
5 Computers & Operations Research
5 Applied Mathematics Letters
5 SIAM Journal on Matrix Analysis and Applications
5 Japan Journal of Industrial and Applied Mathematics
5 Designs, Codes and Cryptography
5 Journal de Théorie des Nombres de Bordeaux
5 Computational and Applied Mathematics
5 Statistics and Computing
4 Discrete Mathematics
4 SIAM Journal on Algebraic and Discrete Methods
4 Circuits, Systems, and Signal Processing
4 Computer Aided Geometric Design
4 The Journal of Supercomputing
4 Computational Statistics
4 SIAM Review
4 Celestial Mechanics and Dynamical Astronomy
4 Engineering Analysis with Boundary Elements
4 LMS Journal of Computation and Mathematics
4 Brazilian Journal of Probability and Statistics
4 Foundations of Computational Mathematics
4 Acta Numerica
4 International Journal of Number Theory
4 BIT. Nordisk Tidskrift for Informationsbehandling
4 Mathematics in Computer Science
4 Research in Number Theory
3 Acta Informatica
3 Astrophysics and Space Science
3 Bulletin of the Australian Mathematical Society
3 Journal of Engineering Mathematics
3 Journal of Fluid Mechanics
3 Lithuanian Mathematical Journal
3 Metrika
3 Physica A
3 Problems of Information Transmission
3 Chaos, Solitons and Fractals
3 ACM Transactions on Mathematical Software
3 Journal of Approximation Theory
3 Journal of Differential Equations
3 Journal of Mathematical Psychology
3 Journal of Soviet Mathematics
3 Journal of Statistical Planning and Inference
3 Mathematical Systems Theory
3 Numerical Functional Analysis and Optimization
3 Proceedings of the American Mathematical Society
3 Transactions of the American Mathematical Society
3 European Journal of Combinatorics
3 Physica D
3 Mathematical and Computer Modelling
...and 293 more Serials
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Cited in 57 Fields

630 Numerical analysis (65-XX)
446 Computer science (68-XX)
282 Number theory (11-XX)
146 Operations research, mathematical programming (90-XX)
136 Statistics (62-XX)
108 Information and communication theory, circuits (94-XX)
105 Linear and multilinear algebra; matrix theory (15-XX)
56 Fluid mechanics (76-XX)
54 Combinatorics (05-XX)
47 Field theory and polynomials (12-XX)
45 Special functions (33-XX)
44 Probability theory and stochastic processes (60-XX)
42 Calculus of variations and optimal control; optimization (49-XX)
41 Approximations and expansions (41-XX)
40 Partial differential equations (35-XX)
32 Commutative algebra (13-XX)
31 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
30 Algebraic geometry (14-XX)
28 Systems theory; control (93-XX)
27 Ordinary differential equations (34-XX)
27 Mechanics of deformable solids (74-XX)
25 Real functions (26-XX)
24 Biology and other natural sciences (92-XX)
22 Mechanics of particles and systems (70-XX)
20 Mathematical logic and foundations (03-XX)
20 Functions of a complex variable (30-XX)
19 Dynamical systems and ergodic theory (37-XX)
18 Statistical mechanics, structure of matter (82-XX)
17 Quantum theory (81-XX)
12 Operator theory (47-XX)
10 Classical thermodynamics, heat transfer (80-XX)
9 Convex and discrete geometry (52-XX)
8 Group theory and generalizations (20-XX)
8 Harmonic analysis on Euclidean spaces (42-XX)
8 Optics, electromagnetic theory (78-XX)
7 General and overarching topics; collections (00-XX)
7 History and biography (01-XX)
7 Difference and functional equations (39-XX)
7 Differential geometry (53-XX)
5 Sequences, series, summability (40-XX)
4 Measure and integration (28-XX)
4 Global analysis, analysis on manifolds (58-XX)
4 Astronomy and astrophysics (85-XX)
4 Geophysics (86-XX)
3 Integral equations (45-XX)
3 Relativity and gravitational theory (83-XX)
2 Integral transforms, operational calculus (44-XX)
2 Geometry (51-XX)
2 Manifolds and cell complexes (57-XX)
1 General algebraic systems (08-XX)
1 Nonassociative rings and algebras (17-XX)
1 Topological groups, Lie groups (22-XX)
1 Abstract harmonic analysis (43-XX)
1 Functional analysis (46-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Mathematics education (97-XX)

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