Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2008 • Question 1

Question

Math 6610 • Analysis of Numerical Methods I Fall 2008 • Question 1

QR factorization Show how to compute the QR factorization of a real \(m\times n\) matrix \(A\) (with \(m\geq n\)) using Householder reflections, and describe how to use the QR factorization to solve the Least Squares problem \[ \|Ax-b\|_2=\min . \tag {1} \]

Raw LaTeX

{QR factorization} Show how to compute the QR factorization of a real
\(m\times n\) matrix \(A\) (with \(m\geq n\)) using Householder reflections, and
describe how to use the QR factorization to solve the Least Squares problem
\[
  \|Ax-b\|_2=\min. \tag{1}
\]

Topic Tags

Cholesky Factorization and SPD Matrices Least Squares and Normal Equations Linear Programming and Optimization QR Factorization