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This course offers an advanced introduction to numerical analysis, with a focus on accuracy and efficiency of numerical algorithms. Topics include sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems), floating-point arithmetic, backwards error analysis, …. Show more.
- Syllabus
This course is an advanced introduction to numerical linear...
- Calendar
Lagrange dual problems 30 Quasi-Newton methods and the BFGS...
- Week 1
How Java’s Floating-Point Hurts Everyone Everywhere (PDF) by...
- Resource Index
Square Roots via Newton’s Method (PDF) Square Roots. Problem...
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MIT OpenCourseWare is a web based publication of virtually...
- Syllabus
This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.
Problems and solutions 1. Problems { Chapter 1 Problem 5.1. Show from rst principles that if V is a vector space (over R or C) then for any set Xthe space (5.1) F(X;V) = fu: X! Vg is a linear space over the same eld, with ‘pointwise operations’. Problem 5.2. If V is a vector space and SˆV is a subset which is closed
11–15. Methods for Ordinary Differential Equations (PDF) 16–20. Fourier Analysis (PDF) 21–25. Spectral Interpolation, Differentiation, Quadrature (PDF) Over 2,500 courses & materials. Freely sharing knowledge with learners and educators around the world. Learn more.
give rough qualitative information about how the graphs of solutions to (1) look geometri-cally. The numerical methods then give the actual graphs to as great an accuracy as desired; the computer does the numerical work, and plots the solutions. 1. Graphical methods.
Numerical analysis provides the foundations for a major paradigm shift in what we understand as an acceptable “answer” to a scientific or techni- cal question.
Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as the solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods.
