R: Least Squares Solution using Householder Transformation

hfti {lsei} | R Documentation

## Least Squares Solution using Householder Transformation

### Description

Solves the least squares problem using Householder forward triangulation with column interchanges. It is an R interface to the HFTI function that is described in Lawson and Hanson (1974, 1995). Its Fortran implementation is public domain and is available at http://www.netlib.org/lawson-hanson.

### Usage

    hfti(a, b, tol=1e-7)

### Arguments

`a` | Design matrix.
`b` | Response vector or matrix.
`tol` | Tolerance for determining the pseudorank.

### Details

Given matrix `a` and vector `b`, `hfti` solves the least squares problem:

minimize || a x - b ||.

### Value

`b` | first `krank` elements contains the solution
`krank` | psuedo-rank
`rnorm` | Euclidean norm of the residual vector.

### Author(s)

Yong Wang <yongwang@auckland.ac.nz>

### References

Lawson and Hanson (1974, 1995). Solving least squares problems. Englewood Cliffs, N.J., Prentice-Hall.

### See Also

`lsei`, `nnls`.

### Examples

    a = matrix(rnorm(10*4), nrow=10)
    b = a %*% c(0,1,-1,1) + rnorm(10)
    hfti(a, b)

[Package lsei version 1.2-0 Index]