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Linear Algebra Decomposition Script
Triangular Decomposition (LU)
triangular_decomp.m
pivot.m
Cholesky Decomposition (LLT )
Cholesky.m
Spectral Decomposition (LDLT)
spectral_decomp.m
Lanczos Tridiagonalization Lanczos_tridiagonal.m

Householder Tridiagonalization,
Four versions

The alternate method uses a more efficient method for the tridiagonalization.

The mo version is optimized for Matlab via sparse matrices.

The Hessenberg version uses Matlab's hess function.

Householder_tridiagonal.m

Householder_tridiagonal_alt.m

Householder_tridiagonal_mo.m

Hessenberg_tridiagonal.m

supporting functions

Standard_Eigen.m

progressbar.m
QR Householder Decomposition QR_Householder.m

Eigenvalues via the QR Householder algorithm.  Two versions.

The mo version is optimized for Matlab via sparse matrices.

QR_Householder_eigen.m

QR_Householder_eigen_mo.m
Generalized eigenvalue problem

eigenvalue.m

Generalized_Eigen.m

Standard_Eigen.m
Single Value Decomposition of a matrix.  Matlab already has a built-in function to do this, but this script demonstrates the steps SVD.m

 Linear Algebra, Matrix Inverse

Matlab Scripts
pseudo inverse of a matrix using two methods:
1. SVD
2. Ben-Israel & Cohen iteration
pseudo_inverse.m
QR Householder Method QR_Householder_inv.m
 Linear Algebra and Eigenvalues Matlab Scripts
This script find the lowest eigenvalue for the generalized eigenvalue problem inverse_power_iteration.m
This script finds the largest eigenvalue for the generalized eigenvalue problem power_iteration.m
Eigenvalues via the QR Householder algorithm QR_Householder_eigen.m
This program converts the generalized eigenvalue problem to a standarized form convert_eig.m
 Modified Gram-Schmidt Orthogonalization modified_Gram_Schmidt.m
Simultaneous iteration example for the generalized eigenvalue problem. simultaneous_iteration.m

Supporting function:
sort_eigenvalues_eigenvectors.m
Subspace Iteration subspace_iteration.m

Supporting function:
sort_eigenvalues_eigenvectors.m
Sturm Sequence for the Generalized Eigenvalue Problem sturm_sequence.m
LDLT.m
Sturm Sequence for the Generalized Eigenvalue Problem.  This is an alternate version which converts the generalized eigenvalue problem to a standard, tridiagonal form.  It is faster for large problems. sturm_sequence_alt.m

Supporting Functions:

convert_general_standard.m
function_Householder_tridiagonal_alt.m


M_K_symmetric.m

eig_power.m
eig_inverse_power.m

diagonal_pivot.m
Sturm_D.m
Mass Condensation (Guyan Reduction)

mass_condensation.m
Generalized_Eigen.m
Single Value Decomposition of a matrix.  Matlab already has a built-in function to do this, but this script demonstrates the procedure SVD.m
Single Value Decomposition of a semi-definite, symmetric matrix SVD_semidefinite_sym.m
pseudo inverse of a matrix using two methods:
1. SVD
2. Ben-Israel & Cohen iteration		 pseudo_inverse.m
Transfer Functions from Modes:
 Transfer Functions Page
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