I am having a problem with a certain inequality I try to understand. I think it's just a basic idia (/trick) I'm missing, but I can't seem to find it. Here's a simplification of …

Find an (approximate) closed-form solution for $S(m, b)$. $$S(m,b)=\sum_{i=0}^{\lfloor (e-1)/2\rfloor}{e \choose i}S(m-1, b-i) \quad + \sum_{i=\lfloor (e-1)/2\rfloor+1}^{\ …

(An earlier version of this at stackexchange got no answers.) Bayesianism says that all uncertainties, or at least all uncertainties about the truth or falsity of propositions, ca …

My main interests are in modern geometry/topology, algebra and mathematical physics. I observe that there is a raising communication, language and social barrier between this commu …

In usual formulation of conjugate gradient algorithm initial search direction is taken to be the residual (so residual and search direction spans Krylov subspace). However, in case …

Is there a practical way to compute the permanent of a large ($91 \times 91$) $(0,1)$ matrix? I have tried to use the matlab function written by Luke Winslow which works great for …

Suppose I have a collection of polynomials with multiple variables (more polynomials than variables, say), and I'm given noisy versions the values of these polynomials at a certain …

I am working on the discrete theory of compressible fluids dynamics, i.e., numerically solving and simulating the compressible fluids , we are interested in the way using discrete …

I am interested in cases where Conjugate gradient works much better than GMRES method. In general, CG is preferable choice in many cases of SPD because it requires less storage an …

Conjugate gradient was originally presented in the 50's before the modern understanding of Krylov subspaces (and the resulting iterative methods) was fully realized. As such, the …

Consider a continuous Markov chain $X = (X_t)$ on a finite state space and let $Q$ be the (given) transition rate matrix. This matrix is very sparse, with non-zero values on 3 diag …

In the context of the Bingham probability distribution the ${ }_1F_1$ hypergeometric function of matrix argument naturally arises as a normalization constant of the probability dis …

I'm implementing a model that requires me to numerically evaluate a multivariate normal integral of the following form $$\int_{-\infty}^\infty \phi(z)\displaystyle\prod_{i=1}^N \ …

I was reading about the Hilbert matrix and Cauchy determinants: \[ \det \left[ \frac{1}{i+j-1} \right]_{i,j} \] By guessing where this determinant is 0 or ∞ we can guess the rig …

It has long been known that the Cauchy initial-value problem for the classical heat equation on $\mathbb{R}$ (or $\mathbb{R}^n$) doesn't have unique solutions, without additional a …