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Steven
Steven
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Given a function $1/(x^2 -k^2)$$1/\sqrt{x^2 -k^2}$ where k is a constant with a small imaginary part, how do you go about constructing a rational approximation? I am interested in the L_p (p=2 or $\infty$) norm of the difference being small on the real line. Both the theoretical and the practical implementation is of interest.

Given a function $1/(x^2 -k^2)$ where k is a constant with a small imaginary part, how do you go about constructing a rational approximation? I am interested in the L_p (p=2 or $\infty$) norm of the difference being small on the real line. Both the theoretical and the practical implementation is of interest.

Given a function $1/\sqrt{x^2 -k^2}$ where k is a constant with a small imaginary part, how do you go about constructing a rational approximation? I am interested in the L_p (p=2 or $\infty$) norm of the difference being small on the real line. Both the theoretical and the practical implementation is of interest.

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Steven
Steven
  • 21
  • 2

Approximation of a given function by rational functions

Given a function $1/(x^2 -k^2)$ where k is a constant with a small imaginary part, how do you go about constructing a rational approximation? I am interested in the L_p (p=2 or $\infty$) norm of the difference being small on the real line. Both the theoretical and the practical implementation is of interest.