program2

program2 - Program 1 Foundations of Computational Math 1...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Program 1 Foundations of Computational Math 1 Fall 2011 Due date: via email by 11:59PM on Friday, 21 October 2011 General Task Consider the matrix A ∈ R n × k with linearly independent columns and the transformation H k H k- 1 ··· H 1 A = parenleftbigg R parenrightbigg where H i , 1 ≤ i ≤ k are Householder reflectors and R ∈ R k × k is a nonsingular upper triangular matrix. Implement a code that is capable of performing this transformation and storing the information about the H i and R efficiently in-place in a 2-dimensional n × k array and a small number of additional 1-dimensional arrays of length n or k . Also implement the necessary additional routines to solve the linear least squares problem min x ∈ R k bardbl b − Ax bardbl 2 given b ∈ R n . You must demonstrate your code on multiple examples with a wide range of values of n , k , and b for three situations: 1. n = k , i.e., a square nonsingular matrix A where x min = A- 1 b . 2. n > k and Ax = b for b ∈ R n and b ∈ R ( A ) i.e., a rectangular matrix A with full column rank and a vector b that define a consistent set of overdetermined equations. 3. n > k and b ∈ R n and b negationslash∈ R ( A ) i.e., a rectangular matrix A with full column rank and a vector b that define a linear least squares problem with a nonzero residual....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

program2 - Program 1 Foundations of Computational Math 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online