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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 |
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2 |
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PDEs (5.7) |
In this lecture, Professor Trefethen discusses Chebyshev spectral discretization. |
Nick Trefethen |
17 Oct 2016 |
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3 |
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PDEs (5.6) |
In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants |
Nick Trefethen |
17 Oct 2016 |
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4 |
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PDEs (5.5) |
In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT. |
Nick Trefethen |
17 Oct 2016 |
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5 |
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PDEs (5.4) |
In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions. |
Nick Trefethen |
17 Oct 2016 |
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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 |
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7 |
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PDEs (5.2) |
In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences. |
Nick Trefethen |
17 Oct 2016 |
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8 |
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PDEs (5.1) |
In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences. |
Nick Trefethen |
17 Oct 2016 |
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9 |
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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 |
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10 |
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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 |
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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 |
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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 |
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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 |
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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 |
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15 |
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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 |
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16 |
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Dense Linear Algebra (2.5) |
In this lecture, Professor Trefethen provides a demonstration of Chebfun. |
Nick Trefethen |
03 Oct 2016 |
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17 |
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Dense Linear Algebra (2.4) |
In this lecture, Professor Trefethen discusses matrix factorizations and SVD. |
Nick Trefethen |
03 Oct 2016 |
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Dense Linear Algebra (2.3) |
In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis. |
Nick Trefethen |
03 Oct 2016 |
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19 |
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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 |
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20 |
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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 |
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21 |
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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 |
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22 |
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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 |
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23 |
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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 |
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24 |
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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 |
