• Publications
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A Regular Layout for Parallel Adders
TLDR
It is shown that addition of n-bit binary numbers can be performed on a chip with a regular layout in time proportional to log n and with area proportional to n.
The Parallel Evaluation of General Arithmetic Expressions
  • R. Brent
  • Mathematics, Computer Science
    JACM
  • 1 April 1974
TLDR
It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log 2 + 10(n - 1) using processors which can independently perform arithmetic operations in unit time.
Fast Algorithms for Manipulating Formal Power Series
TLDR
This paper shows that the composition and reversion problems are equivalent (up to constant factors), and gives algorithms which require only order (n log n) ~/2 operations in many cases of practical importance.
Almost linear-time computation of the singular value decomposition using mesh-connected processors
A cyclic Jacobi method for computing the singular value decomposition of an $mxn$ matrix $(m \geq n)$ using systolic arrays is proposed. The algorithm requires $O(n^{2})$ processors and $O(m + n \log
The Solution of Singular-Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays
Parallel Jacobi-like algorithms are presented for computing a singular-value decomposition of an $m \times n$ matrix $(m \geqq n)$ and an eigenvalue decomposition of an $n \times n$ symmetric matrix.
An Algorithm with Guaranteed Convergence for Finding a Zero of a Function
  • R. Brent
  • Mathematics, Computer Science
    Comput. J.
  • 1971
TLDR
An algorithm is presented for finding a zero of a function which changes sign in a given interval using linear interpolation and inverse quadratic interpolation with bisection and ALGOL 60 procedures.
Fast Multiple-Precision Evaluation of Elementary Functions
  • R. Brent
  • Mathematics, Computer Science
    JACM
  • 1 April 1976
TLDR
It is shown that ƒ(x) can be evaluated, with relative error, in the Schönhage-Strassen bound on M(n), the number of single-precision operations required to multiply n-bit integers.
Some Efficient Algorithms for Solving Systems of Nonlinear Equations
We compare the Ostrowski efficiency of some methods for solving systems of nonlinear equations without explicitly using derivatives. The methods considered include the discrete Newton method,
Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants
TLDR
It is proved that entries in the Pade table can be computed by the Extended Euclidean Algorithm, and an algorithm EMGCD (Extended Middle Greatest Common Divisor) is described which is faster than the algorithm HGCD of Aho, Hopcroft and Ullman, although both require time O(n log2 n).
An improved Monte Carlo factorization algorithm
TLDR
A cycle-finding algorithm is described which is about 36 percent faster than Floyd's (on the average), and applied to give a Monte Carlo factorization algorithm which is similar to Pollard's but about 24 percent faster.
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