We show that the common symbolic manipulation tasks of computing multiple partial derivatives, definite integration, and definite summation, are #P-hard, i.e., at least as hard as counting the accepting input strings for any Turing machine that halts in polynomial time. (The “multiple partial derivatives” part was previously known.)

  We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibili...

Abstract Logical forgetting is removing some variables from a formula while maintaining its consequences on the remaining variables. This removal may require exponential time arbitrary propositional Horn formulae, but it only takes polynomial single-head definite formulae. Single-head means that no variable head of multiple clauses. An algorithm to make if possible shown. It enlarges set formul...

A semi-definite programming (SDP) formulation of the multi-objective economic-emission dispatch problem is presented. The fuel cost and emission functions are represented by high order polynomial functions and this was shown to be a more accurate representation of the economic-emission dispatch (EED) problem. Furthermore, the polynomial functions of both objective functions are aggregated into ...

Let A be an n×n positive definite Hermitian matrix with all eigenvalues between 1 and 2. We represent the permanent of as integral some explicit log-concave function on R2n. Consequently, there is a fully polynomial randomized approximation scheme (FPRAS) for perA.

We study the eigenvalues and eigenspaces of the quadratic matrix polynomial Mλ + sDλ + K as s → ∞, where M and K are symmetric positive definite and D is symmetric positive semi-definite. The work is motivated by its application to modal analysis of finite element models with strong linear damping. Our results yield a mathematical explanation of why too strong damping may lead to practically un...

We develop a computationally efficient approximation of the maximum likelihood (ML) detector for 16 Quadrature Amplitude Modulation (16QAM) in multiple input multiple output (MIMO) systems. The detector is based on a semi definite relaxation (SDR) of the ML problem. The resulting optimization is a semi definite program (SDP) which can be solved in polynomial time with respect to the number of i...

We show that for fixed A,B, hermitian nonnegative definite matrices, and fixed k the coefficients of the t in the polynomial Tr(A + tB) is positive if TrAB > 0 and m > N(A,B, k).

The problem of finding a nonzero solution linear recurrence Ly=0 with polynomial coefficients where y has the form definite hypergeometric sum, related to Inverse Creative Telescoping Problem Chen and Kauers (2017)[Sec. 8], now been open for three decades. Here we present an algorithm (implemented in SageMath package) which, given such quasi-triangular, shift-compatible factorial basis B=〈Pk(n)...

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets centers that are not determining for polynomials. It shown polynomial consistence sufficient in order to define kernel-based numerical the functional usual properties optimal recovery. Application examples include generation sparse differentiation formulas Laplacian a grid accurate ...