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1 - 8 of 8
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 Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Kaltofen E., Villard G. Journal of Computational and Applied Mathematics 162(1): 133-146, 2004. Type: Article
The common way of computing det A is via LU factorization of the n × n matrix A with pivoting, or via QR fa...
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May 7 2004 |
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When are two numerical polynomials relatively prime?
Beckermann B., Labahn G. Journal of Symbolic Computation 26(6): 677-689, 1998. Type: Article
The authors discuss testing the relative primality of twopolynomials that are given with inexact coefficients or, in other words,testing whether two polynomials will always remain relatively prime (orcoprime) even if their coefficients...
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Jul 1 1999 |
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Testing shift-equivalence of polynomials by deterministic, probabilistic and quantum machines
Grigoriev D. Theoretical Computer Science 180(1-2): 217-228, 1997. Type: Article
Two polynomials f ( X ) and g ( X ) are shift-equivalent if f ( X + a ) = g ( X ) for some shift a. Testing the shift-equivalence of two polynomials is a natur...
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Dec 1 1997 |
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An extended polynomial GCD algorithm using Hankel matrices
Sendra J., Llovet J. Journal of Symbolic Computation 13(1): 25-39, 1992. Type: Article
Connections between computing the extended Euclidean scheme for two polynomials f ( x ) and g ( x ) of degree n (ending with their greatest common divisor (gcd)) and solving Hank...
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Feb 1 1993 |
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Lower bounds for the complexity of polynomials
Stoss H. Theoretical Computer Science 64(1): 15-23, 1989. Type: Article
The linear substitution argument of the early sixties (Knuth [1]) leads to sharp lower bounds on the complexity of polynomial evaluation over any field of constants for almost all polynomials of a fixed degree, excluding an algebraic v...
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Mar 1 1990 |
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Multiplicative complexity of polynomial multiplication over finite fields
Kaminski M., Bshouty N. Journal of the ACM 36(1): 150-170, 1989. Type: Article
To evaluate the coefficients of the product of two polynomials of degree n, one may evaluate these polynomials at 2 n + 1 points (such as the ( 2 n + 1 )th roots of 1 ), then pai...
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Sep 1 1989 |
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A linear time algorithm for residue computation and a fast algorithm for division with a sparse divisor
Kaminski M. Journal of the ACM 34(4): 968-984, 1987. Type: Article
The residue p(x) mod q(x) of a polynomial p(x) of degree nn modulo a polynomial q(x) of degree O(log n) is computed over a finite field in O(n) ...
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Jun 1 1988 |
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Lectures on the complexity of bilinear problems
de Groote H., Springer-Verlag New York, Inc., New York, NY, 1987. Type: Book (9789780387172057)
In the wide area of the evaluation of a set of bilinear forms, which includes computing the products of two complex numbers, two integers, two matrices, two polynomials, and two polynomials modulo a third one (for more examples see [1]...
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Mar 1 1988 |
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