Numerical Linear Algebra
MA 514
Spring, 2018
M-Files
| Filename | Description |
| adi_pre.m |
Implements ADI
preconditioning. |
| bc_vectors_DD.m |
Called by ras.m to create
vectors of the subdomain boundary solution values. |
| biharmonic_op.m |
Creates the matrix for the
biharmonic operator discretized on a regular mxn grid on a
rectangle. |
| census_model.m |
Models census data with
polynomials determined using linear least-squares. |
| condif.m |
Creates the matrix for the convection-diffusion operator discretized on an mxn grid on a rectangle. |
| condif_DD.m |
Creates the matrix for the
convection-diffusion operator on subdomains when called by
ras.m. |
| dampedSpringSystem.m |
Determines eigenvalues for the damped
spring system in Ex. 4.1 of Demmel book and shows their
movement with increasing damping. |
| demo_pcg.m |
Performs preconditioned
conjugate gradient iterations when called by pcg_demo.m. |
| fill_in_demo.m |
Demonstrates fill-in when
Cholesky and incomplete Cholesky decomposition are applied
to a sparse matrix. |
| funHW4.m | Evaluates the right-hand side function in Homework 4 and several subsequent homeworks. |
| gaussseidel.m | Implements the Gauss-Seidel method. |
| ge_naive.m |
Performs
naive Gaussian elimination on a square matrix. |
| ge_pp.m |
Performs
Gaussian elimination with partial pivoting on a square
matrix. |
| ge_solve.m |
Solves
Ax = b, given the output of Gaussian elimination, either
naive or with partial pivoting. |
| gmres_demo.m |
Demonstrates the
performance of restarted GMRES without and with
preconditioning. |
| gmres514.m |
Implements restarted GMRES.
|
| householder_examples.m |
Provides examples of
forming Householder transformations and using them to
obtain a QR decomposition. |
| imaging_demo.m |
Demonstrates basic usage of MATLAB in image
viewing and manipulation and of the SVD in image
compression. Requires the image file MsPotatoHead.JPG. |
| it_method_demo.m |
Demonstrates the
performance of Jacobi, Gauss-Seidel, or SOR on a
discretized Poisson problem. |
| jacobi.m |
Implements Jacobi
iteration. |
| ks_method_demo.m |
Demonstrates the
performance of the MATLAB Krylov solvers with various
preconditioners. |
| laplacian.m |
Creates the matrix for the
Laplacian operator discretized on a regular mxn grid on a
rectangle. |
| loadrhs.m |
Creates the right-hand side
vector for a Poisson or convection-diffusion problem. |
| MsPotatoHead.JPG |
Image file for use with imaging_demo.m. |
| pcg_demo.m |
Demonstrates the
performance of the
preconditioned conjugate gradient method. |
| poisson_rb_reordering.m |
Produces the permutation
matrix for converting the "natural" variable ordering for
the 2D Poisson problem to red-black ordering. |
| poisson_sor_analyzer.m |
Produces the spectral radius
of the iteration matrix for Jacobi, Gauss-Seidel, and SOR
with the optimal relaxation parameter, together with a
graph of the spectral radius of the SOR iteration matrix
as the parameter ranges from zero to two. |
| ras.m |
Implements restricted
additive Schwarz for the convection-diffusion problem. |
| rhsfun.m |
Evaluates the right-hand side function in several homework assignments. |
| seesol.m |
Creates a surface plot of
the solution of a 2D Poisson problem. |
| sor.m |
Implements SOR. |
| squareDrum.m |
Computes normal modes of vibration of a
"square drum" on the unit square in the plane. |
