A Chebyshev polynomial interval-searching method (``Lanczos economization'') for solving a nonlinear equation with application to the nonlinear eigenvalue problem
Assume that we want to compute some zeros of a function \(f\) and that the evaluation of \(f(x)\) for a given value of \(x\) is expensive. In this case it may be better to first compute zeros of a polynomial approximation \(f_ N\) than to apply Newton's method directly. This is elucidated for the computation of eigenvalues via zeros of determinants. \{Reviewer's remark: The computation of eigenvalues via the characteristic polynomial can be recommended only in some well-known special cases.\}.
Chebyshev polynomial interval-searching method
scientific article; zbMATH DE number 758610