We consider the max-plus analogue of the eigenproblem for matrix pencils, A ⊗ x = λ⊗ B ⊗ x. We show that the spectrum of (A, B) (i.e., the set of possible values of λ), which is a finite union of intervals, can be computed in pseudopolynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introdu...

-Now a day’s security is very essential measure during the data transmission ,in this paper we are proposing an efficient mechanism of group key protocol and high complex cryptographic algorithm. we consider how the chaotic maps can be improved to fulfill the cryptographic demands. To achieve this, we extend the domain of Chebyshev maps from real number set to finite field. Based on this extens...

The masks for Loop’s triangle subdivision surface algorithm are modified resulting in surfaces with bounded curvature and the convex hull property. New edge masks are generated by a cubic polynomial mask equation whose Chebyshev coefficients are closely related to the eigenvalues of the corresponding subdivision matrix. The mask equation is found to satisfy a set of smoothness constraints on th...

In this paper we propose an explicit solution to the polynomial least squares approximation problem on Chebyshev extrema nodes. We also show that the inverse of the normal matrix on this set of nodes can be represented as the sum of two symmetric matrices: a full rank matrix which admits a Cholesky factorization and a 2-rank matrix. Finally we discuss the numerical properties of the proposed fo...

Absrracr-The low sensitivity property of lossless discrete integrator (LDI) low-pass ladder filters is shown to be preserved in lossless discrete differentiator (LDD) high-pass ladder filters 111. The exact design method for LDI ladder filters given in [Z] is further developed by introducing a set of closed-form design formulas for digital ah-pole Chebyshev transfer functions. A new technique f...

We construct an hyperinterpolation formula of degree n in the three-dimensional cube, by using the numerical cubature formula for the product Chebyshev measure given by the product of a (near) minimal formula in the square with Gauss-Chebyshev-Lobatto quadrature. The underlying function is sampled at N ∼ n/2 points, whereas the hyperinterpolation polynomial is determined by its (n + 1)(n + 2)(n...

In paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. In this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is rem...

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by...

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...

We exhibit a numerical technique based on Newton’s method for finding all the roots of Legendre and Chebyshev polynomials, which execute less iterations than the standard Newton’s method and whose results can be compared with those for Chebyshev polynomials roots, for which exists a well known analytical formula. Our algorithm guarantees at least nine decimal correct ciphers in the worst case, ...