Lecture 4 Flashcards
What is a LLS (Linear Least Squares) problem? What notation is used?
What is the meaning of span(A)?
What can be said about span(A) when Ax - b is minimized?
How is span(A) is orthogonal to Ax - b used to derive the normal equations?
How can be shown that always a minimum for Ax -b can be found?
What is the rank(A), how is this connected to the uniqueness of the minimizer of Ax - b?
How can ||Ax - b|| be minimized? What are two remarks?
What is the idea of orthogonal vectors?
Ze staan haaks op elkaar
When is a vector orthogonal? When is a matrix orthogonal? How does an orthogonal matrix affect the length?
What does QR factorization produce?
How can QR decomposition be used for LLS?
What is the concept of reduced QR decomposition?
How to decompose a vector into an orthogonal and a parallel element?
What is the idea behind the Gram-Schmidt method?
What is the Gram-Schmidt algorithm?
What is the modified Gram-Schmidt algorithm? Why is it used?
It increases stability.
What is the main idea behind Householder reflections?
What is the Householder QR factorization algorithm?
