The widespread habit of “plugging” arbitrary symmetric functions as kernels in support vector machines (SVMs) often yields good empirical classification results. However, in case of non conditionally positive definite (non-cpd) functions they are hard to interpret due to missing geometrical and theoretical understanding. In this paper we provide a step towards comprehension of SVM classifiers i...

The error estimates for nite volume element method applied to and D non de nite problems are derived A simple upwind scheme is proven to be unconditionally stable and rst order accurate Mathematics Subject Classi cation N Introduction The purpose of this note is three fold We would like to extend the results due to Bank and Rose Hackbusch Cai and McCormick and Jianguo and Shitong to D problems ...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

We construct, analyze and implement SSOR-like preconditioners for non-Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew-Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR-like iteration methods as well as the cor...

We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements can be arbitrarily corrupted by large additive noise. Given that the problem is highly non-convex, we propose a simple semidefinite programming relaxation t...

where x is a vector of displacements of structural coordinates, M is a positive definite mass matrix, C is a non-negative definite damping matrix, and K is a non-negative definite stiffness matrix. The nonlinear restoring forces are given in R(x, ẋ) and f ext(t) is a vector of external dynamic loads. At any point in time, t = ti+1 = (i+ 1)h, we may solve for the accelerations in terms of the di...

Abstract We show that adjustable robust linear programs with affinely box data uncertainties under separable polynomial decision rules admit exact sums of squares (SOS) reformulations. These problems share the same optimal values and a one-to-one correspondence between solutions. A sum representation non-negativity non-convex over plays key role in reformulation. This reformulation allows us to...