In this paper, we want to find a continuous function fitting through the discrete covariance sequence generated by stationary AR process. This can be determined as soon Yule–Walker equations are found. The procedure consists of two steps. At first inverse zeros characteristic polynomial process must fixed. second step is based on fact that an also seen difference equation. By solving equation, ...

The spectral properties of Hermitian matrix polynomials with real eigenvalues have been extensively studied, through classes such as the definite or definitizable pencils, definite, hyperbolic, or quasihyperbolic matrix polynomials, and overdamped or gyroscopically stabilized quadratics. We give a unified treatment of these and related classes that uses the eigenvalue type (or sign characterist...

The Line Sum Scaling problem for a nonnegative matrix A is to find positive definite diagonal matrices Y , Z which result in prescribed row and column sums of the scaled matrix Y AZ. The Matrix Balancing problem for a nonnegative square matrix A is to find a positive definite diagonal matrix X such that the row sums in the scaled matrix XAX are equal to the corresponding column sums. We demonst...

We construct a probabilistic polynomial time algorithm that computes the mixed discriminant of given n positive definite n × n matrices within a 2O(n) factor. As a corollary, we show that the permanent of an n×n nonnegative matrix and the mixed volume of n ellipsoids inRn can be computed within a 2O(n) factor by probabilistic polynomial time algorithms. Since every convex body can be approximat...

We construct near-optimal coresets for kernel density estimate for points in Rd when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size O( √ d log(1/ε)/ε), and we show a near-matching lower bound of size Ω( √ d/ε). The upper bound is a polynomial in 1/ε improvement when d ∈ [3, 1/ε2) (for all kernels except the Gaussian kernel which had a ...

discoverer, developed under Maple, is a package aiming at discovering and proving inequality-type theorems. It can discover new inequalities automatically, without requiring us to put forward any conjectures beforehand. It is also applied to the classification of the real physical solutions of geometric constraint problems. Many inequalities with various backgrounds have been discovered or re-d...

When σ is a quasi-definite moment functional with the monic orthogonal polynomial system {Pn(x)}∞n=0, we consider a point masses perturbation τ of σ given by τ := σ+ λ ∑m l=1 ∑ml k=0((−1) ulk/k!)δ (x− cl), where λ, ulk, and cl are constants with ci = cj for i = j. That is, τ is a generalized Uvarov transform of σ satisfying A(x)τ = A(x)σ, where A(x) = ∏m l=1(x− cl) l. We find necessary and suff...

We study real algebraic plane curves, at an elementary level, using as little algebra as possible. Both cases, affine and projective, are addressed. A real curve is infinite, finite or empty according to the fact that a minimal polynomial for the curve is indefinite, semi–definite nondefinite or definite. We present a discussion about isolated points. By means of the operator, these points can ...