Fundamentals of Numerical Mathematics for Physicists and Engineers. Alvaro Meseguer

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Название Fundamentals of Numerical Mathematics for Physicists and Engineers
Автор произведения Alvaro Meseguer
Жанр Математика
Серия
Издательство Математика
Год выпуска 0
isbn 9781119425755



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have a reliable measure of how fast (or slow) a method converges to the desired solution. Some readers may think that we are taking an alarming position since the bisection and Newton Matlab codes provide the solution almost instantaneously, the difference in speed between both methods in terms of computational time being unnoticeable. However, we will see in Part II that the efficiency of the method becomes much more relevant when solving systems of nonlinear equations.

      A rigorous way of measuring quantitatively the performance of an iterative method is given by the concept of order of convergence:

      Order of Convergence: A root‐finding method providing a sequence images with images has order of convergence images if

      for some positive bounded constant images, usually termed as the asymptotic error constant. In particular, if images, then images must be smaller than unity for the criterion to be applicable.

      which means that for large enough images,