Variational methods for nonlinear eigenvalue problems associated with thermal ignition

A Chebyshev Polynomial Interval-Searchin

A Chebyshev Polynomial Interval-Searching Method ("Lanczos Economization") for Solving a Nonlinear Equation with Application to the Nonlinear Eigenvalue Problem

✍ John P. Boyd 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 362 KB

To search a given real interval for roots, our algorithm is to replace \(f(\lambda)\) by \(f_{N}(\lambda)\), its \(N\)-term Chebyshev expansion on the search interval \(\lambda \in\left[\lambda_{\min }, \lambda_{\max }\right]\), and compute the roots of this proxy. This strategy is efficient if and