We present a Chebyshev-Davidson method to compute a few smallest positive eigenvalues and corresponding eigenvectors of the linear response eigenvalue problem. The method is actually applicable to the slightly more general linear response eigenvalue problem where purely imaginary eigenvalues may occur. For the Chebyshev filter, a tight upper bound is obtained by a computable bound estimator con...

This pa per suggests a simple valuation method based on Chebyshev approximation at Chebyshev nodes to value American put options. It is similar to the approach taken in Sullivan (2000), where the option`s continuation region function is estimated by using a Chebyshev polynomial. However, in contrast to Sullivan (2000), the functional is fitted by using Chebyshev nodes. The suggested method is f...

Stable polynomial evaluation and interpolation at n Chebyshev or adjusted (expanded) Chebyshev points is performed using O(nlog’ n) arithmetic operations, to be compared with customary algorithms either using on the order of n* operations or being unstable. We also evaluate a polynomial of degree d at the sets of n Chebyshev or adjusted (expanded) Chebyshev points using O(dlog d log n) if n 5 d...

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...

Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...

In Euclidean spaces, the geometric notions of nearest-points map, farthestpoints map, Chebyshev set, Klee set, and Chebyshev center are well known and well understood. Since early works going back to the 1930s, tremendous theoretical progress has been made, mostly by extending classical results from Euclidean space to Banach space settings. In all these results, the distance between points is i...

In this paper, a Chebyshev spectral collocation domain decomposition (DD) semidiscretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s–Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation...

Abstract—In Digital Signal Processing, one of the most important filter type is the FIR filter which can be designed via various methods. Window technique is the most important technique that is used to design the FIR filter. Apart from various window techniques, Dolph-Chebyshev window has the subject of importance for the design of the FIR filter in efficient way. In this paper, the design met...

In this paper‎, two inverse problems of determining an unknown source term in a parabolic‎ equation are considered‎. ‎First‎, ‎the unknown source term is ‎estimated in the form of a combination of Chebyshev functions‎. ‎Then‎, ‎a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem‎. ‎For solving the problem‎, ‎the operational matrices of int...