Minimax Models in the Theory of Numerical Methods

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Camilli, C. AA S. Cacace, M. Falcone: A dynamic domain decomposition for the eikonal-diffusion equation , Discrete and Continuous Dynamical Systems - Series S, 9 , no. Cristiani, M. Falcone: Can local single-pass methods solve any stationary Hamilton-Jacobi-Bellman equation? Cristiani, D.

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D'Eustacchio: Myrmedrome: simulating the life of an ant colony , in M. Emmer Ed. Between Culture and Mathematics, Springer, S. Falcone: Numerical approximation of Nash equilibria for a class of non-cooperative differential games , in L. Petrosjan e V. Mazalov Eds.

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Numerical analysis shares some of the attractions of both pure and applied mathematics. For its derivations and analysis it draws on many areas of pure mathematics, yet its objective is practical - to produce reliable numerical approximations, and to do so efficiently. Practical experience of numerical computation is essential for a full understanding of the successes and failures of particular numerical methods.


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The practical sessions for this course form part of the assessment and are designed to allow you to experiment with a variety of numerical methods through the programming language Python. Aim: To introduce the basic framework of the subject, enabling the student to solve a variety of problems and laying the foundation for further investigation of particular areas in the Levels 3 and 4.

For details of prerequisites, corequisites, excluded combinations, teaching methods, and assessment details, please see the Faculty Handbook. For information about use of calculators and dictionaries in exams please see the Examination Information page in the Degree Programme Handbook.

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Department of Mathematical Sciences. Outline of Course Aim: To introduce the basic framework of the subject, enabling the student to solve a variety of problems and laying the foundation for further investigation of particular areas in the Levels 3 and 4. Term 1 Introduction 1 lecture : The need for numerical methods. Statement of some problems which can be solved by techniques described in this course.

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What is Numerical Analysis? Non-Linear Equations 7 lectures : Bracketing and bisection.

Fixed-point theorem and convergence of fixed-point iteration. Error analysis and order. The Newton-Raphson formula. Aitken's method.

Zhang , Zhou : Minimax rates of community detection in stochastic block models

Sets of non-linear equations. Newton iteration, without analysis of convergence. Errors 2 lectures : Rounding error and truncation error. The Optimal Consumption Ramsey Model 9.

Inventory Dynamic Optimization 9. COV Constrained Problems 9. Bang-Bang Control Problems Consumption Model Investment Model Inventory Optimization Two State Variables Control Problems Current-Value Hamiltonian Multiperiod Production Models with Linear Programming Wagner-whitin Algorithm for Inventory Dynamic Modelling Basic Descriptive Statistics Numerical Integration.

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Paperback ISBN: Imprint: Academic Press.



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