Classicaly, the Hilbert class polynomial P∆ ∈ Z[X] of an imaginary quadratic discriminant ∆ is computed using complex analytic techniques. In 2002, Couveignes and Henocq [5] suggested a p-adic algorithm to compute P∆. Unlike the complex analytic method, it does not suffer from problems caused by rounding errors. In this paper we complete the outline given in [5] and we prove that, if the Genera...

task graph scheduling is a multi-objective optimization and np-hard problem. in this paper a new algorithm on homogeneous multiprocessors systems is proposed. basically, scheduling algorithms are targeted to balance the two parameters of time and energy consumption. these two parameters are up to a certain limit in contrast with each other and improvement of one causes reduction in the other on...

distribution centers (dcs) play important role in maintaining the uninterrupted flow of goods and materials between the manufacturers and their customers.this paper proposes a mathematical model as the bi-objective capacitated multi-vehicle allocation of customers to distribution centers. an evolutionary algorithm named non-dominated sorting ant colony optimization (nsaco) is used as the optimi...

Nakajima and Tanaka showed that the algebraic eigenvalue problem occurring in the discrete ordinate and matrix operator methods can be reduced to finding eigenvalues and eigenvectors of the product of two symmetric matrices, one of which is positive definite. Here, we show that the Cholesky decomposition of this positive definite matrix can be used to convert the eigenvalue problem into one inv...

Relations between the off thermal equilibrium dynamical process of on-line learning and the thermally equilibrated off-line learning are studied for potential gradient descent learning. The approach of Opper to study on-line Bayesian algorithms is used for potential based or maximum likelihood learning. We look at the on-line learning algorithm that best approximates the off-line algorithm in t...

A restarted nonsymmetric Lanczos algorithm is given for computing eigenvalus and both right and left eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Restarting also makes it possible to deal with roundoff error in new ways. We give a scheme for avoiding near-breakdown and discuss maintaining biorthogonality. A system of linear equations can be solved s...

Fujishige proposed a polynomial-time maximum flow algorithm using maximum adjacency (MA) orderings. Computational results by Fujishige and Isotani showed that the algorithm was slower in practice than Goldberg and Tarjan’s algorithm. In this paper we propose an improved version of Fujishige’s algorithm using preflows. Our computational results show that the improved version is much faster than ...

Optimization of the exploitation operation is one of the most important issues facing the mining engineers. Since several technical and economic parameters depend on the cut-off grade, optimization of this parameter is of particular importance. The aim of this optimization is to maximize the net present value (NPV). Since the objective function of this problem is non-linear, three methods can b...

The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature. A recent application of the Lanczos algorithm proposed by Bai, Fahey and Golub allows quadrature evaluation of inner products of the form ψ · ...

In this paper we present a parallel algorithm for the symmetric algebraic eigenvalue problem. The algorithm is based upon a divide and conquer scheme suggested by Cuppen for computing the eigensystem of a symmetric tridiagonal matrix. We extend this idea to obtain a parallel algorithm that retains a number of active parallel processes that is greater than or equal to the initial number througho...