Package numericalMethods.algebra.linear.decompose

Algorithms related to decomposition of matrices and their determinants.

See:
          Description

Class Summary
Cholesky Computes the cholesky decomposition of a symmetric positive-definite Matrix and can therefore test whether a symmetric matrix is positive-definite.
Householder Computes for a matrix A the matrices Q and R complying A=QR.
LR Computes for a square matrix A the matrices L and R complying A=LR.
PLR Computes for a square matrix A the matrices P, L and R complying PA=LR.
QR Computes for a square matrix A the matrices Q and R complying A=QR.
TestCholesky  
TestHouseholder  
TestLR  
TestPLR  
TestQR  
TestTridiagonal  
Tridiagonal Transforms a symmetric matrix into triadiagonal form.
Unmerge Seperates merged matrices.
 

Package numericalMethods.algebra.linear.decompose Description

Algorithms related to decomposition of matrices and their determinants.

All algorithms are offered in an efficient version (using as few resources as possible but having sometimes difficult arguments) and in an inefficient version (that has therefore easy to use arguments).

The following table gives an overview of the different decomposition algorithms (sorted by speed - fastest first, slowest last):

class advantages disadvantages minimal resources algorithm
LR · very fast
· no additional resources
· when successful gives determinant
· does not decompose all regular matrices
· no control on condition of triangular matrices
· one matrix
Gauss
PLR · fast
· no additional resources
· gives determinant
· no control on condition of triangular matrices
· one matrix
· one vector
Gauss with pivoting
QR · triangular matrix has never worse condition than original matrix
· gives ||determinant||
· not very fast
· sometimes not good-natured
· two matrices
Gram-Schmidt
Householder · always good-natured
· few additional resources
· works on non-square matrices (more rows than columns)
· gives determinant
· not very fast
· one matrix
· one vector
· one temporary vector
Householder