R: LU Decomposition of Square Matrix

lu.decomposition {matrixcalc} | R Documentation

## LU Decomposition of Square Matrix

### Description

This function performs an LU decomposition of the given square matrix argument the results are returned in a list of named components. The Doolittle decomposition method is used to obtain the lower and upper triangular matrices

### Usage

    lu.decomposition(x)

### Arguments

`x` | a numeric square matrix

### Details

The Doolittle decomposition without row exchanges is performed generating the lower and upper triangular matrices separately rather than in one matrix.

### Value

A list with two named components.

`L` | The numeric lower triangular matrix
`U` | The number upper triangular matrix

### Author(s)

Frederick Novomestky fnovomes@poly.edu

### References

Bellman, R. (1987). Matrix Analysis, Second edition, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics.

Golub, G. H. and C. F. Van Loan (1996). Matrix Computations, Third Edition, John Hopkins University Press

Horn, R. A. and C. R. Johnson (1985). Matrix Analysis, Cambridge University Press.

### Examples

    A <- matrix( c ( 1, 2, 2, 1 ), nrow=2, byrow=TRUE)
    luA <- lu.decomposition( A )
    L <- luA$L
    U <- luA$U
    print( L )
    print( U )
    print( L %*% U )
    print( A )
    B <- matrix( c( 2, -1, -2, -4, 6, 3, -4, -2, 8 ), nrow=3, byrow=TRUE )
    luB <- lu.decomposition( B )
    L <- luB$L
    U <- luB$U
    print( L )
    print( U )
    print( L %*% U )
    print( B )

[Package matrixcalc version 1.0-3 Index]