A Chebyshev polynomial interval-searching method (“Lanczos economization”) for solving a nonlinear equation with application to the nonlinear eigenvalue problem

@inproceedings{Boyd1995ACP,
  title={A Chebyshev polynomial interval-searching method (“Lanczos economization”) for solving a nonlinear equation with application to the nonlinear eigenvalue problem},
  author={John P. Boyd},
  year={1995}
}
Abstract To search a given real interval for roots, our algorithm is to replace f(λ) by f N (λ) , its N-term Chebyshev expansion on the search interval λ ∈ [λ min , λ max ], and compute the roots of this proxy. This strategy is efficient if and only if f(λ) itself is expensive to evaluation, such as when f(λ) is the determinant of a large matrix whose elements depend nonlinearly on λ. For such expensive functions, it is much cheaper to search for zeros of f N (λ) , which can be evaluated in O(N… CONTINUE READING

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