# Tagged Questions

The tag has no usage guidance.

349 views

In 1971, Thomson and Freede generalized the Lidskii-Wielandt inequalites as follows (version for singular values) Let $A$, $B$ be $n\times n$ Hermitian matrices. Suppose $\alpha_1\geq \alpha_2 \geq \... 0answers 123 views ### What is the technical difference between a deformation and a perturbation? What is the technical difference between a deformation and a perturbation? Do they exist in somewhat different categories? 0answers 197 views ### Error bound on matrix vector multiplication I am multiplying a matrix$A$with vector$p$. However, the matrix$A$isn't accurate. Some (a very small fraction) of the element's value is changed from$a_{i,j}$to {0,$-a_{i,j}$,$2a_{i,j}$}. ... 0answers 99 views ### Perturbation analysis for three term recurrences Jacobi polynomials, denoted by$J^{(\alpha,\beta)}_n$, on$[-1,1]$satisfy a three term recurrence $$J_{n+1}^{(\alpha,\beta)}(x) = (A_n+B_nx)J^{(\alpha,\beta)}_n + C_nJ_{n-1}^{(\alpha,\beta)}(x), \... 0answers 86 views ### Perturbation method of a boundary value problem Let u(x, \epsilon, \theta) be the solution of$$u''+(\epsilon \cos(x)+\theta-u)u=0$$with boundary conditions$u'(0)=0$and$u'(\pi)=0$. Here$\theta\in [0, 1]$. I tried to put the solution in ... 0answers 121 views ### How does perturbation method guarantee its solution for the perturbed pde$\Delta u + \epsilon u^2 =0$[This may not be a research-level question; if it violates any term of this website, I will delete it right away] My question is quite simple: Suppose we are given a PDE of with a boundary condition$...
Consider a non-linear operator $\cal H$ which maps a function to a function (e.g., a map from a starting wave function $f(x,y,z)$ to a later wave function according to some non-linear PDE) and an \$\...