Complexity of factorization and GCD computation for linear ordinary differential operatorsdoi:10.1007/BF01104106This paper presents an algorithm of polynomial complexity for finding greatest common (right) divisors of families of linear ordinary differential operators. An algorithm is presented for ...
The GCD problem for more than two numbers is interesting in its own right. Thus, we can use Euclid's algorithm recursively to compute the GCD of more than two numbers. Also, we can do a constructive computation, the so-called extended GCD, which expresses the GCD as a linear combination...
Seidenberg, is of non-elementary complexity. In the description of the algorithm an important procedure is construction of a polynomial-time algorithm for finding the greatest common divisor of a family of polynomials in one variable with parametric coefficients. The GCD is itself a polynomial in ...
An algorithm for the reduction of a matrix of integers to triangular form with power complexity of the computations. We introduce a new parallel algorithm LZMP for computing the Lempel-Ziv complexity of a string of characters from a finite alphabet. The LZ-complexity is a... MA Frumkin - 《...
You are using Eucledian algorithm for GCD. Here is wikipedia article for algorithmic efficieny for this. Share Improve this answer Follow answered Jun 9, 2013 at 7:49 Aseem Bansal 6,9421414 gold badges4949 silver badges8686 bronze badges Add a comment Your Answer Sign up or log in...
sum of n numbers:O(1)def sum_total(n): return int(n*(n+1)/2)LCM/GCD:(Euclid's algorithm)def gcd(a,b): if a == 0: return b return gcd(b%a,a) def lcm(a,b): prod = a*b hcf = gcd(a,b) return prod//hcfOdd-Even:O(1)...
Successive matrix squaring algorithm for computing the Drazin inverse 2000, Applied Mathematics and Computation Show abstract Some complexity results for polynomial ideals 1997, Journal of Complexity Show abstract Optimal and nearly optimal algorithms for approximating polynomial zeros 1996, Computers and Mathe...
We obtain new results regarding the precise average bitcomplexity of five algorithms of a broad Euclidean type. We develop a general framework for analysis of algorithms, where the average-case complexity of an algorithm is seen to be related to the analytic behaviour in the complex plane of the...
This is the first L(3) algorithm whose running time (without fast integer arithmetic) provably grows only quadratically with respect to log B, like Euclid's gcd algorithm and Lagrange's two-dimensional algorithm. 展开 关键词: lattice reduction L(3) floating-point arithmetic DOI: 10.1137/...
The algorithm exploits the reduction of the problem to integer division; the polynomial remainder and quotient are recovered from integer remainder and quotient via binary segmentation. (iv) The latter approach is also extended to the sequential evaluation of the gcd of two polynomials over integers....