Fall 2008

R. J. Braun

Matlab example codes.

Rounding and Convergence

Zoom.m Rounding in polynomial evaluation (Van Loan)

Zoom2.m Rounding in polynomial evaluation (Van Loan)

Zoom4.m Combining the previous two files in a format suitable for using publish in Matlab

Mysum1.m Summation

Quad1.m: Quadratic formula with loss of significance

Quad2.m: More Robust roots from quadratic equation

Linear Systems

Function 2.1: forwardsub.m

Backward substitution: backsub.m

Function 2.2: lufact.m

Pathological matrix for partial pivoting

lu_time_ex.m luscalar.m lurowvect.m lumatlevel.m

Special Matrices

Script with diagonally dominant matrices

Script to make banded matrices

Script to try sparse matrices

Script to make sparse matrices

Least Squares

Normal equations approach

QR factorization

QR factorization for least squares

Example for Project 2 Example image

Eigenvalue problems

QR iteration example diary file

Shifted QR iteration function

Shifted QR iteration with deflation for all eigenvalues

Inefficient Hessenberg reduction

Shifted QR iteration function with Hessenberg reduction test version (with iteration count)

Shifted QR iteration function without Hessenberg reduction test version (with iteration count)

Number of iterations per eigenvalue Max number of iterations for a set of matrices

SVD and an image

Iterative methods

Fill-in with two standard matrices and with luinc

Power method function

Shifted inverse power method function

Arnoldi iteration function

arngmres.m: Simple gmres function

gmress.m: Simple gmres function like last one but more compact (vectorized)

Gmres example

Different Krylov variants

Preconditioning examples 1

Rootfinding

N^(-4) convergence example Quadratic convergence example (note plot)

Illustration of Newton method

Function 6.1, Newton method function

Function 6.2, Secant method function

Function 6.3, Bisection method function

Function 6.4, Newton method for systems function

Department of Mathematical Sciences