General references: S.D. Conte & C. de Boor, Elementary Numerical Analysis: An Algorithmic Approach, Third edition, 1981. McGraw-Hill. L.F. Shampine, R.C. Allen, Jr & S. Pruess, Fundamentals of Numerical Computing, 1997. Wiley. This course is concerned with the same problems as Numerical Analysis I, but the mathematical content is greater. In the interests of simplicity and brevity, the use of ...

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This set of notes covers topics that most commonly show up on the Numerical Analysis qualifying exam in the Mathematics department at UCLA. Each section covers a specific area of numerical analysis. At the end of each section, we provide a list of key theorems. If the proof of the theorem is directly relevant to the qualifying exam, it will be included in this document. Otherwise, we simply inc...

These notes are in development and only for internal use at the University of Mancheser. For questions, comments or typos please e-mail [email protected]. The following books were used for the preparation of these lecture notes. • C. Brenner and L.R. Scott, The mathematical theory of finite element methods, Springer • C. Gasquet and P. Witomski, Fourier Analysis and Applications, Spr...

A backward analysis of integration methods, whose numerical solution is a P-series, is presented. Such methods include Runge-Kutta methods, partitioned Runge-Kutta methods and Nystrr om methods. It is shown that the numerical solution can formally be interpreted as the exact solution of a perturbed diierential system whose right-hand side is again a P-series. The main result of this article is ...

Multi-level Monte Carlo is a relatively new method that computes expectations of stochastic processes to a desired tolerance significantly faster than previous methods. I will detail the basic idea of multi-level Monte Carlo and show how to implement it in the continuous time Markov chain setting, which is a modeling choice commonly used in the biosciences. Departments of Computer Science, Math...