Trigonometric Polynomial Interpolation of Images

On a Fast Convergence of the Rational-Trigonometric-Polynomial Interpolation

We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to th...

Hermite Interpolation Using ERBS with Trigonometric Polynomial Local Functions

Symbolic-Numeric Sparse Polynomial Interpolation in Chebyshev Basis and Trigonometric Interpolation

We consider the problem of efficiently interpolating an “approximate” black-box polynomial p(x) that is sparse when represented in the Chebyshev basis. Our computations will be in a traditional floating-point environment, and their numerical sensitivity will be investigated. We also consider the related problem of interpolating a sparse linear combination of “approximate” trigonometric function...

Monotone Rational Trigonometric Interpolation

This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...

When Is a Trigonometric Polynomial Not a Trigonometric Polynomial?

for some nonnegative integer k and complex numbers a0, . . . , ak, b1, . . . , bk ∈ C. Trigonometric polynomials and their series counterparts, the Fourier series, play an important role in many areas of pure and applied mathematics and are likely to be quite familiar to the reader. When reflecting on the terminology, however, it is reasonable to wonder why the term trigonometric polynomial is ...