An Algorithm Based on the Fft for a Generalized Chebyshev Interpolation

نویسندگان

  • TAKEMITSU HASEGAWA
  • HIROSHI SUGIURA
چکیده

An algorithm for a generalized Chebyshev interpolation procedure, increasing the number of sample points more moderately than doubling, is presented. The FFT for a real sequence is incorporated into the algorithm to enhance its efficiency. Numerical comparison with other existing algorithms is given.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems

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...

متن کامل

On Group Fourier Analysis and Symmetry Preserving Discretizations of PDEs

In this paper we review some group theoretic techniques applied to discretizations of PDEs. Inspired by the recent years active research in Lie groupand exponential time integrators for differential equations, we will in the first part of the article present algorithms for computing matrix exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetri...

متن کامل

A Fast Algorithm for Chebyshev, Fourier & Sinc Interpolation Onto an Irregular Grid

A Chebyshev or Fourier series may be evaluated on the standard collocation grid by the Fast Fourier Transform (FFT). Unfortunately, the FFT does not apply when one needs to sum a spectral series at N points which are spaced irregularly. The cost becomes O(N2) operations instead of the FFT's O(N log N). This sort of "off-grid" interpolation is needed by codes which dynamically readjust the grid ...

متن کامل

A Fast Algorithm for Chebyshev, Fourier, and Sine Interpolation onto an Irregular Grid

A Chebyshev or Fourier series may be evaluated on the standard collocation grid by the fast Fourier transform (FFT). Unfortunately, the FFT does not apply when one needs to sum a spectral series at N points which are spaced irregularly. The cost becomes O(N’) operations instead of the FFTs O(N log N). This sort of “off-grid” interpolation is needed by codes which dynamically readjust the grid e...

متن کامل

A polynomial interpolation process at quasi-Chebyshev nodes with the FFT

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 ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010