Lanczos Approximation - Coefficients

Coefficients

The coefficients are given by

$p_k(g) = \sum_{a=0}^k C(2k+1, 2a+1) \frac{\sqrt{2}}{\pi} \left(a - \begin{matrix} \frac{1}{2} \end{matrix} \right)! {\left(a + g + \begin{matrix} \frac{1}{2} \end{matrix} \right)}^{- \left( a + \frac{1}{2} \right) } e^{a + g + \frac{1}{2} }$

with denoting the (i, j)th element of the Chebyshev polynomial coefficient matrix which can be calculated recursively from the identities

Paul Godfrey describes how to obtain the coefficients and also the value of the truncated series A as a matrix product.

Read more about this topic: Lanczos Approximation