CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019

Lecture 21 (last time)Uses of matrix functions for graphsUses of generalized eigenvalues andhow to compute generalize eigenvalues.A new class of methods to solve Ax=bcalled “Krylov methods”CG, MINRES, SYMMLQ, GMRES, LSQRThese methods search for the bestsolution over a subspace and theywill always be better thanRichardson, Steepest Descent, etc.Then we hyper-optimize theimplementations, which really differbetween symemtric and non-symmetric.This will give us new algs for eigenvalues and eigenvectors too!These methods have many interpretations;- polynomials- subspaces and optimization- conjugate directions (e.g. CG)

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CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019 CS 515 - Purdue University - Computer Science - David F. Gleich - 2019

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