I have to solve a least squares problem:$$x=\arg \min\|Ax-b\|$$where $A$ is a $m\times n$ matrix, $m>n$, and $b\in\mathbb{R}^m$. I always thought that doing this via QR factorization is better than solving the normal equations $$A^*Ax=A^*b$$directly. However, I am now in the situation where the columns of $A$ are close to orthogonal and my code is significantly faster (factor 10) when using normal equation. Just to be sure I am doing nothing wrong, is this a reasonable result? ($A$ has size $20000\times 2000$. Computing the Gramian matrix takes longer than solving the normal equation)
Least Squares: Numerically, is solving normal equations okay for nice matrices?
linear algebra;least squares