In this data-based paper we report on our experiments in factoring integers from 50 to 200 bits with the postsieving phase of NFS as a potential application. We implemented and compared several general-purpose factoring algorithms suited for these smaller numbers, from Shanks’s square form factorization method to the self-initializing quadratic sieve, and revisited the older continued fraction ...

AMS subject classifications: 62E15 60E05 Keywords: Bivariate exponential distributions Bivariate chi-square distributions Correlated quadratic forms a b s t r a c t We introduce a class of absolutely continuous bivariate exponential distributions, generated from quadratic forms of standard multivariate normal variates. This class is quite flexible and tractable, since it is regulated by two par...

We propose an algorithm for finding zero divisors in quaternion algebras over quadratic number fields, or equivalently, solving homogeneous quadratic equations in three variables over Q( √ d) where d is a square-free integer. The algorithm is deterministic and runs in polynomial time if one is allowed to call oracles for factoring integers and polynomials over finite fields.

We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary. In some cases, the square root algorithm runs in Õ(log q) bit operations over finite fields with q elements. As an application, we construct a deterministic primality-proving al...

We analyze alternating descent algorithms for minimizing the sum of a quadratic function and block separable non-smooth functions. In case the quadratic interactions between the blocks are pairwise, we show that the schemes can be accelerated, leading to improved convergence rates with respect to related accelerated parallel proximal descent. As an application we obtain very fast algorithms for...

We consider a generalized proximal point method for solving variational inequalities with maximal monotone operators in a Hilbert space. It proves to be that the conditions on the choice of a non-quadratic distance functional depend on the geometrical properties of the operator in the variational inequality, and – in particular – a standard assumption on the strict convexity of the kernel of th...

Quadratic regression functionals are important for bandwidth selection of nonparametric regression techniques and for nonparametric goodness-of-t test. Based on local polynomial regression , we propose estimators for weighted integrals of squared derivatives of regression functions. The rates of convergence in mean square error are calculated under various degrees of smoothness and appropriate ...

A common requirement in optimal control problems arising autonomous navigation is that the decision variables are constrained to be outside certain sets. Such set exclusion constraints represent obstacles must avoided by motion system. This paper presents a simple and efficient method for solving optimization with general implicit constraints. The embeds quadratic penalty framework solves inner...

This article is a study of congruence conditions, modulo powers of two, on class number of real quadratic number fields Q(vu), for which d has at most thtee distinct prime divisors. Techniques used are those associated with Gaussian composition of binary quadratic forms. 1. Let hid) denote the class number of the quadratic field Qi\ß) and let h id) denote the number of classes of primitive bina...

a meshless approach, collocation discrete least square (cdls) method, is extended in this paper, for solvingelasticity problems. in the present cdls method, the problem domain is discretized by distributed field nodes. the fieldnodes are used to construct the trial functions. the moving least-squares interpolant is employed to construct the trialfunctions. some collocation points that are indep...