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In numerical analysis it is common to approximate a solution to a PDE $$u'(t) = (A+B) u(t), \quad u(0)=u_0$$ which is just given by $e^{t(A+B)}u_0$ by the splitting $e^{tB/2} e^{tA} e^{tB/2}u_0.$ Here,...

Consider the discrete second derivative with Dirichlet boundary conditions on $\mathbb C^n$. Its eigendecomposition is fully known: see wikipedia It seems like the largest eigenvalue $\lambda_1$ is ...

Let $K$ be a compact self-adjoint operator on a Hilbert space $H$ such that for some normalized $x \in H$ and $\lambda \in \mathbb C:$ $\Vert Kx-\lambda x \Vert \le \varepsilon.$ It is well-known ...