Complex Chebyshev alterations

Computing rational Gauss-Chebyshev quadrature formulas with complex poles

We provide a fast algorithm to compute arbitrarily many nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [−1, 1]. This algorithm is based on the derivation of explicit expressions for the Chebyshev (para-)orthogonal rational functions.

Chebyshev acceleration techniques for large complex non hermitian eigenvalue problems

The computation of a few eigenvalues and the corresponding eigenvectors of large complex non hermitian matrices arises in many applications in science and engineering such as magnetohydrodynamic or electromagnetism [6], where the eigenvalues of interest often belong to some region of the complex plane. If the size of the matrices is relatively small, then the problem can be solved by the standa...

Real vs Complex Rational Chebyshev Approximation on an Interval

Real VS. Complex Rational Chebyshev Approximation on an Interval

I f f E C[-I, I] is real-valued, let Er( f ) and E'( f ) be the errors in best approximation to f in the supremum norm by rational functions of type ( m , n ) with real and complex coefficients, respectively. It has recently been observed that E'( f ) < Er( f ) can occur for any n > 1, but for no n 1 is it known whether y,,,, = inf, E'( f ) / E r ( f ) is zero or strictly positive. Here we show...

A Fast Algorithm for Linear Complex Chebyshev Approximations

We propose a new algorithm for finding best minimax polynomial approximations in the complex plane. The algorithm is the first satisfactory generalization of the well-known Remez algorithm for real approximations. Among all available algorithms, ours is the only quadratically convergent one. Numerical examples are presented to illustrate rapid convergence.