1. Numerical Linear Algebra

Direct Solvers — Quiz

Test your understanding of direct solvers with 5 practice questions.

Practice Questions

Question 1

Which QR factorization algorithm is most numerically stable for computing an orthonormal basis of a matrix?

Question 2

Which direct solver factorization is appropriate for a symmetric but indefinite matrix $A$?

Question 3

Perform a Cholesky factorization on the matrix $A=\begin{pmatrix}4&2\\\\2&3\end{pmatrix}$. What is the lower-triangular factor $L$?

Question 4

In the economy-size (thin) QR factorization of an $m\times n$ matrix $A$ with $m>n$, what are the dimensions of the matrix $Q$?

Question 5

Compared to full QR factorization, what is the primary memory advantage of the economy-size QR factorization?