Читать книгу Fundamentals of Numerical Mathematics for Physicists and Engineers - Alvaro Meseguer - Страница 22

For an authoritative study of different root‐finding methods for nonlinear scalar equations, I strongly recommend Dahlquist and Björk's Numerical Methods in Scientific Computing, Vol. I. The reader will find there detailed mathematical proofs of the convergence of many algorithms, as well as other very important topics that have not been covered in this chapter, such as Fixed‐Point Iteration, Minimization or the solution of algebraic equations and deflation. That chapter also addresses the Termination Criteria problem (i.e. when to stop the iteration) in depth and with mathematical rigor.

For a different approach to the root‐finding problem, Acton's Numerical Methods that Work is an alternative. The reader will find in that text very clear geometrical explanations of why different root‐finding methods may have convergence problems. Acton's book also provides deep insight into the technical aspects of root‐finding algorithms, as well as very useful tips and strategies.