gibson:teaching:fall-2016:iam961
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gibson:teaching:fall-2016:iam961 [2016/09/02 07:49] gibson |
gibson:teaching:fall-2016:iam961 [2016/11/04 12:03] (current) gibson [Homework and exercises] |
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| Numerical linear algebra is the science of solving systems of linear equations $Ax=b$ and the eigenvalue problem $A v = \lambda v$ on a digital computer --problems are at the root of the vast bulk of scientific computation. Compared to classical linear algebra, the finite precision and computational cost of numerical mathematics brings in a number of important new concepts, including conditioning, stability, and accuracy, and efficiency. We will develop these ideas and learn the most important numerical linear algebra algorithms: QR, LU, SVD decompositions, Gramm-Schmidt orthogonalization, the QR eigenvalue algorithm, and Krylov subspace methods. Time permitting, we will also study key algorithms for function optimization and the solution of systems of nonlinear equations. | Numerical linear algebra is the science of solving systems of linear equations $Ax=b$ and the eigenvalue problem $A v = \lambda v$ on a digital computer --problems are at the root of the vast bulk of scientific computation. Compared to classical linear algebra, the finite precision and computational cost of numerical mathematics brings in a number of important new concepts, including conditioning, stability, and accuracy, and efficiency. We will develop these ideas and learn the most important numerical linear algebra algorithms: QR, LU, SVD decompositions, Gramm-Schmidt orthogonalization, the QR eigenvalue algorithm, and Krylov subspace methods. Time permitting, we will also study key algorithms for function optimization and the solution of systems of nonlinear equations. | ||
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| + | This semester we will also be exploring the [[http://www.julialang.org| Julia scientific programming language]]. Julia is the future of scientific computing. Get on board now! | ||
| Text: [[https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefethen/dp/0898713617/| Numerical Linear Algebra]], by Trefethen and Bau, SIAM Press. I strongly recommend that you buy a paper copy of this book. It's only $50. | Text: [[https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefethen/dp/0898713617/| Numerical Linear Algebra]], by Trefethen and Bau, SIAM Press. I strongly recommend that you buy a paper copy of this book. It's only $50. | ||
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| [[gibson:teaching:fall-2016:iam961:grades | Grades ]] | [[gibson:teaching:fall-2016:iam961:grades | Grades ]] | ||
| - | ^ HW/EX ^ Julia notebook ^ due ^ topic ^ comments ^ | + | ==== Homework and exercises ==== |
| - | | [[gibson:teaching:fall-2016:iam961:ex1]] | | | | | | + | |
| + | Homeworks will be turned in a graded; exercises are work you should do but not turn in. | ||
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| + | ^ HW/EX ^ due ^ topic ^ comments ^ | ||
| + | | [[gibson:teaching:fall-2016:iam961:ex1]] | | getting started with Julia | | | ||
| + | | [[gibson:teaching:fall-2016:iam961:hw1]] | W 09/14 | linear algebra | reviewish | | ||
| + | | [[gibson:teaching:fall-2016:iam961:hw2]] | M 10/03 | SVD | | | ||
| + | | [[http://nbviewer.jupyter.org/url/www.channelflow.org/iam961/iam961-hw3.ipynb|HW3]]| M 11/21 | QR, stability, accuracy | [[gibson:teaching:fall-2016:iam961:julia_notebook_howto|Julia notebook how-to]] | | ||
gibson/teaching/fall-2016/iam961.1472827758.txt.gz · Last modified: 2016/09/02 07:49 by gibson
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