Polynomial approximations in the complex plane
Copyright policy )Polynomial approximations in the complex plane
The Lanczos \(\tau\)-method yields polynomial approximations for analytic functions which satisfy linear differential equations with polynomial coefficients. In particular, if the perturbation is proportional to the Faber or Chebyshev polynomials of a specific region G, then the method produces near-minimax polynomial approximations on G. The paper reports on approximations for the exponential and for the Bessel functions on circular sectors \(\{| z|
- Durham University United Kingdom
Applied Mathematics, truncated Chebyshev series, Lanczos tau-method, Approximation in the complex plane, Bessel functions, approximations for the exponential, Computational Mathematics, General theory of numerical methods in complex analysis (potential theory, etc.), Computation of special functions and constants, construction of tables, Algorithms for approximation of functions, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Chebyshev polynomials, polynomial approximations for analytic functions
Applied Mathematics, truncated Chebyshev series, Lanczos tau-method, Approximation in the complex plane, Bessel functions, approximations for the exponential, Computational Mathematics, General theory of numerical methods in complex analysis (potential theory, etc.), Computation of special functions and constants, construction of tables, Algorithms for approximation of functions, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Chebyshev polynomials, polynomial approximations for analytic functions
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