All Questions

For my research I need to solve a generalised eigenvalue problem $Ax=\lambda B x$, where $A$, $B$ are general matrices, and selectively find only eigen-pairs $\lambda, x$ such that $\lambda\in \mathbb{...

Full zero-error SVD on an $m \times n$ matrix $A$ would cost $O(\min(m^2n,mn^2))$. What is the time complexity if we need only the largest singular value and its corresponding vectors? I think it is $...

I am interested in efficient numerical procedures for solving large-scale instances of the following projected minimum-eigenvalue problem: $$\mu := \min_{v \in \mbox{ker}(A)} \frac{v^T H v}{\lVert v \...

I am trying to write a QR algorithm in Python for eigenvectors and eigenvalues finding for large symmetric matrices, My initial thought was to use Householder transformation with a Wilkinson shift ...

Let $\Sigma$ be an $n \times n$ correlation matrix whose least eigenvalue is denoted by $\lambda$. $\Sigma_i'$ be an $(n-1) \times (n-1)$ submatrix of $\Sigma$ obtained by eliminating the $i$-th row ...

Let $G$ be a symmetric and indefinite matrix defined as follows $$ G := S - \begin{pmatrix} I_n & I_n \\ I_n & I_n \end{pmatrix},$$ where $S$ is a symmetric positive definite matrix of size $...