gibson:teaching:fall-2015:iam961
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gibson:teaching:fall-2015:iam961 [2015/09/29 13:06] gibson |
gibson:teaching:fall-2015:iam961 [2016/09/02 08:53] (current) gibson |
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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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| Text: //Numerical Linear Algebra//, by Trefethen and Bau, SIAM Press. | Text: //Numerical Linear Algebra//, by Trefethen and Bau, SIAM Press. | ||
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| ^ lecture notes ^ date ^ | ^ lecture notes ^ date ^ | ||
| - | ^ HW ^ due ^ topic ^ comments ^ | + | ^ HW ^ Julia notebook ^ due ^ topic ^ comments ^ |
| - | | {{:gibson:teaching:fall-2015:iam961:iam961-hw1.pdf|HW1}} | 9/21 | fundamentals | | | + | | {{:gibson:teaching:fall-2015:iam961:iam961-hw1.pdf|HW1}} | | 9/21 | fundamentals | | |
| - | | [[:gibson:teaching:fall-2015:iam961:iam961-hw2|HW2]] | 10/05 | SVD | | | + | | [[:gibson:teaching:fall-2015:iam961:iam961-hw2|HW2]] | | 10/05 | SVD | | |
| + | | {{:gibson:teaching:fall-2015:iam961:hw3.pdf|HW3}} | {{:gibson:teaching:fall-2015:hw3.ipynb|}} | 11/02 | QR | [[:gibson:teaching:fall-2015:iam961:ijulia_howto|how to use the IJulia notebook]] | | ||
| + | | HW4 | {{:gibson:teaching:fall-2015:iam961:hw4p1.ipynb|HW4-p1}} {{:gibson:teaching:fall-2015:iam961:hw4p2.ipynb|HW4-p2}}| 12/17 | Eigval and Krylov | | ||
| ^ exam ^ date ^ comments ^ | ^ exam ^ date ^ comments ^ | ||
| | midterm | t.b.d | | | | midterm | t.b.d | | | ||
| | final | t.b.d. | | | | final | t.b.d. | | | ||
gibson/teaching/fall-2015/iam961.1443557216.txt.gz · Last modified: 2015/09/29 13:06 by gibson
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