The question whether every operator on H has an hyperinvariant subspace is one of the most difficult problems in operator theory. The purpose of this paper is to make a beginning on the hyperinvariant subspace problems for another class of operators closely related to the normal operators namely, the class of k -quasi-class A operators. A necessary and sufficient condition for the hypercyclicit...

Interpolation polynomial pn at the Chebyshev nodes cosπj/n (0 ≤ j ≤ n) for smooth functions is known to converge fast as n → ∞. The sequence {pn} is constructed recursively and efficiently in O(n log2 n) flops for each pn by using the FFT, where n is increased geometrically, n = 2i (i = 2, 3, . . . ), until an estimated error is within a given tolerance of ε. This sequence {2j}, however, grows ...

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set checkerboard nodes. This generalizes existing results at Padua nodes, Chebyshev Morrow-Patterson and Geronimus We also construct subspace spanned by linearly independent vanishing that vanish nodes prove uniqueness in quotient space defined as with certain degree over polynomials.

The electron spin resonance (ESR) of nanoscale molecular magnet V15 is studied. Since the Hamiltonian of V15 has a large Hilbert space and numerical calculations of the ESR signal evaluating the Kubo formula with exact diagonalization method is difficult, we implement the formula with the help of the random vector technique and the Chebyshev polynominal expansion, which we name the double Cheby...

Abstract. This paper discusses a method based on Laguerre polynomials combined with a Filtered Conjugate Residual (FCR) framework to compute the product of the exponential of a matrix by a vector. The method implicitly uses an expansion of the exponential function in a series of orthogonal Laguerre polynomials, much like existing methods based on Chebyshev polynomials do. Owing to the fact that...

We study interpolation polynomials based on the points in [−1, 1]× [−1, 1] that are common zeros of quasi-orthogonal Chebyshev polynomials and nodes of near minimal degree cubature formula. With the help of the cubature formula we establish the mean convergence of the interpolation polynomials. 1991 Mathematics Subject Classification: Primary 41A05, 33C50.

In this paper a new technique is proposed for the clustering and classification of spatio-temporal object trajectories extracted from video motion clips. The trajectories are represented as motion time series and modelled using Chebyshev polynomial approximations. Trajectory clustering is then performed to discover patterns of similar object motion. The coefficients of the basis functions are u...

Chebyshev functions, which are equiripple in a certain domain, are used to generate equiripple halfband lowpass frequency responses. Inverse Fourier transformation is then used to obtain explicit formulas for the corresponding impulse responses. The halfband lowpass FIR digital filters designed in this way are quasi-equiripple, having performances very close to those of true equiripple filters,...

When solving the Symmetric Positive Definite (SPD) linear system Ax = b with the conjugate gradient method, the smallest eigenvalues in the matrix A often slow down the convergence. Consequently if the smallest eigenvalues in A could be somehow “removed”, the convergence may be improved. This observation is of importance even when a preconditioner is used, and some extra techniques might be inv...