Relevant Links
Nicholas Trefethen, FRS is professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford.
| # | Episode Title | Description | People | Date | |
|---|---|---|---|---|---|
| 1 | 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 |
| 2 | Creative Commons | PDEs (5.7) | In this lecture, Professor Trefethen discusses Chebyshev spectral discretization. | Nick Trefethen | 17 Oct 2016 |
| 3 | 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 |
| 4 | 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 |
| 5 | 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 |
| 6 | 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 |
| 7 | Creative Commons | PDEs (5.2) | In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences. | Nick Trefethen | 17 Oct 2016 |
| 8 | 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 |
| 9 | 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 |
| 10 | 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 |
| 11 | 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 |
| 12 | 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 |
| 13 | 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 |
| 14 | 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 |
| 15 | 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 |
| 16 | Creative Commons | Dense Linear Algebra (2.5) | In this lecture, Professor Trefethen provides a demonstration of Chebfun. | Nick Trefethen | 03 Oct 2016 |
| 17 | Creative Commons | Dense Linear Algebra (2.4) | In this lecture, Professor Trefethen discusses matrix factorizations and SVD. | Nick Trefethen | 03 Oct 2016 |
| 18 | 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 |
| 19 | 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 |
| 20 | 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 |
| 21 | 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 |
| 22 | 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 |
| 23 | 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 |
| 24 | 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 |