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Suppose $A$ is a triangular matrix. What is the most efficient known algorithm to compute the polynomial (in $x$) matrix $(xI-A)^{-1}$? Of course, $(xI-A)^{-1}= N(x)/p_A(x)$, where $p_A$ is the ...

In the dynamic mode decomposition, we consider a sequence of data vectors $\{z_0, \dots, z_m\}$ where $z_k \in \mathbb{R}^n$ for all $n$. We assume that the data satisfies the linear relationship $z_{...

I have two systems $$ A \vec{x} = f(\vec{x}, \vec{y}), \:\:\: A \vec{y} = g(\vec{x}, \vec{y}) $$ Both have the same constant, square, invertible matrix $A$. I implemented an iterative algorithm with ...