Edit Profile (opens in new tab) Brent, Richard Peirce Co-Author Distance Author ID: brent.richard-peirce Published as: Brent, Richard P.; Brent, R. P.; Brent, Richard; Brent, Richard Peirce more...less External Links: MGP · ORCID · Wikidata · Twitter · dblp · GND · IdRef · theses.fr Documents Indexed: 145 Publications since 1970, including 4 Books and 12 Additional arXiv Preprints 1 Contribution as Editor · 1 Further Contribution Co-Authors: 78 Co-Authors with 91 Joint Publications 2,342 Co-Co-Authors 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 all top 5 Fields 64 Number theory (11-XX) 64 Numerical analysis (65-XX) 48 Computer science (68-XX) 17 Combinatorics (05-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 11 Special functions (33-XX) 11 Information and communication theory, circuits (94-XX) 7 Approximations and expansions (41-XX) 5 History and biography (01-XX) 5 Field theory and polynomials (12-XX) 4 General and overarching topics; collections (00-XX) 4 Probability theory and stochastic processes (60-XX) 3 Functions of a complex variable (30-XX) 3 Operations research, mathematical programming (90-XX) 2 Integral transforms, operational calculus (44-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Mathematics education (97-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 all top 5 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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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