README

Harvard Applied Math 205: Code Examples
Unit 5: Eigenvalue Problems
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square_eig.py - Demonstrates Python's "eigs" function for finding the
eigenvalues and eigenvectors of a sparse matrix. Calculates fundamental
mode vibrations on a square drum, described by the 2D wave equation.

power_method.py - Demonstrates the shifted power method for extracting
an eigenvector of a matrix.

rayleigh_iter.py - Demonstrates the Rayleigh quotient method for rapidly
estimating an eigenvalue.

qr_example.py - Demonstrates the QR method for finding eigenvalues and
eigenvectors.

lanczos.py - Demonstrates the Lanczos algorithm (an example of a Krylov
subspace method) for estimating a subset of eigenvalues.

poisson_cg.py - Solves the Poisson equation on a square using the conjugate
gradient method.