We consider the quadratic eigenvalue problem (QEP) (λ2A+λB+ C)x = 0, where A,B, and C are Hermitian with A positive definite. The QEP is called hyperbolic if (x∗Bx)2 > 4(x∗Ax)(x∗Cx) for all nonzero x ∈ Cn. We show that a relatively efficient test for hyperbolicity can be obtained by computing the eigenvalues of the QEP. A hyperbolic QEP is overdamped if B is positive definite and C is positive ...

1. Introduction In this paper we generalize the parallelized lambda method for computing invariants in real qua-dratic function elds. A basic such invariant is the regulator, which plays an important role in cryptosystems based on real quadratic function elds. For example, in the key-exchange protocol by Scheidler, Stein and Williams SSW96], the regulator provides a measure for the key space; m...

where q = e. Let d ≡ 0, 3 (mod 4) be a positive integer, so that −d is a negative discriminant. Denote by Qd the set of positive definite integral binary quadratic forms Q(x, y) = ax + bxy + cy = [a, b, c] with discriminant −d = b − 4ac, including imprimitive forms (if such exist). We let αQ be the unique complex number in the upper half plane H which is a root of Q(x, 1) = 0. Values of j at th...

The comprehensive numerical study has been made here for the solution of One dimensional heat equation the Finite Element method is adopted for the solution with B-spline basis function the important finding of the present study is to understand the basics behind the FEM method while the B-spline basis function come into the picture here the solution is made using Quadratic B-spline and Cubic B...

such that N is a solution to s of the congruences. (It is, of course, clear that no Ar can be a solution to more than s of the congruences (1).) Examples : On the one extreme there is the Sieve of Eratosthenes for finding all primes p in the range A = B12 ^ p < B, where ti = m, — 1 for all i. (Here to, are all the primes < Bl .) On the other extreme there is the Chinese remainder type of proble...

The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computational bottleneck in real-world data analysis. We propose a novel algorithm for KP...

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

Abstract: This paper proposes a new algorithm for solving Mixed-Integer Quadratic Programming (MIQP) problems. The algorithm is particularly tailored to solving small-scale MIQPs such as those that arise in embedded hybrid Model Predictive Control (MPC) applications. The approach combines branch and bound (B&B) with nonnegative least squares (NNLS), that are used to solve Quadratic Programming ...

Suppose that X t = P 1 j=0 c j Z t?j is a stationary linear sequence with regularly varying c j 's and with innovations fZ j g that have innnite variance. Such a sequence can exhibit both high variability and strong dependence. The quadratic form Q n = P n t1s=1 b (t ? s)X t X s plays an important role in the estimation of the intensity of strong dependence. In contrast with the nite variance c...

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...