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numerical analysis

# Episode Title Description People Date
1 Derivation of the time-dependent Hartree(-Fock)-equation In the talk I will present recent progress in proving closeness of the microscopic and effective description for systems of many fermions. Peter Pickl 21 Oct 2016
2 Creative Commons PDEs (5.8) In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms? Nick Trefethen 17 Oct 2016
3 Creative Commons PDEs (5.7) In this lecture, Professor Trefethen discusses Chebyshev spectral discretization. Nick Trefethen 17 Oct 2016
4 Creative Commons PDEs (5.6) In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants Nick Trefethen 17 Oct 2016
5 Creative Commons PDEs (5.5) In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT. Nick Trefethen 17 Oct 2016
6 Creative Commons PDEs (5.4) In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions. Nick Trefethen 17 Oct 2016
7 Creative Commons PDEs (5.3) In this lecture, Professor Trefethen discusses order of accuracy and reaction-diffusion equations and other stiff PDEs. Nick Trefethen 17 Oct 2016
8 Creative Commons PDEs (5.2) In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences. Nick Trefethen 17 Oct 2016
9 Creative Commons PDEs (5.1) In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences. Nick Trefethen 17 Oct 2016
10 Creative Commons ODEs and Nonlinear Dynamics (4.4) In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun. Nick Trefethen 17 Oct 2016
11 Creative Commons ODEs and Nonlinear Dynamics (4.3) In this lecture, Professor Trefethen discusses planetary motions, chaos and Lyapunov exponents, the Lorenz equations, and lastly Sinai billiards and the SIAM 100-digit challenge. Nick Trefethen 17 Oct 2016
12 Creative Commons ODEs and Nonlinear Dynamics (4.2) In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes. Nick Trefethen 17 Oct 2016
13 Creative Commons ODEs and Nonlinear Dynamics (4.1) In this lecture, Professor Trefethen discusses ODEs and IVPs, Runge-Kutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun. Nick Trefethen 17 Oct 2016
14 Creative Commons Optimization (3.3) In this lecture, Professor Trefethen discusses NEOS and COIN-OR, constraints and linear programming, and quadratic programming and linear constraints. Nick Trefethen 03 Oct 2016
15 Creative Commons Optimization (3.2) In this lecture, Professor Trefethen discusses Newton's methods for minimizing a function of several variables. He then moves on from Newton's method to practical optimization. Nick Trefethen 03 Oct 2016
16 Creative Commons Optimization (3.1) In this lecture, Professor Trefethen discusses Newton's methods for 1) a single equation, 2) a system of equations, and 3) minimizing a function of 1 variable. Nick Trefethen 03 Oct 2016
17 Creative Commons Dense Linear Algebra (2.5) In this lecture, Professor Trefethen provides a demonstration of Chebfun. Nick Trefethen 03 Oct 2016
18 Creative Commons Dense Linear Algebra (2.4) In this lecture, Professor Trefethen discusses matrix factorizations and SVD. Nick Trefethen 03 Oct 2016
19 Creative Commons Dense Linear Algebra (2.3) In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis. Nick Trefethen 03 Oct 2016
20 Creative Commons Dense Linear Algebra (2.2) In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear least-squares. Nick Trefethen 03 Oct 2016
21 Creative Commons Dense Linear Algebra (2.1) In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices. Nick Trefethen 03 Oct 2016
22 Creative Commons Sparse Matrices and Iterative Methods (1.4) In this lecture, Professor Trefethon provides a definition of numerical analysis and provides an overview of matrix iterations, including a discussion on the Lanczos iteration. He also reviews various numerical software tools and information sources. Nick Trefethen 03 Oct 2016
23 Creative Commons Sparse Matrices and Iterative Methods (1.3) In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners Nick Trefethen 03 Oct 2016
24 Creative Commons Sparse Matrices and Iterative Methods (1.2) In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG. Nick Trefethen 03 Oct 2016
25 Creative Commons Sparse Matrices and Iterative Methods (1.1) In this lecture, Professor Trefethen first provides an overview of the field of linear algebra and optimization. Secondly, he discusses the question of how fast we can solve Ax=3Db? Thirdly, he discusses sparse matrices Nick Trefethen 03 Oct 2016