Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients

Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients

This article deals with the efficient (approximate) inversion of finite element stiffness matrices of general second-order elliptic operators with L∞-coefficients. It will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices (H-matrices). Furthermore, numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear co...

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

Carleman estimates and unique continuation for second order elliptic equations with nonsmooth coefficients

Strichartz Estimates for Second Order Hyperbolic Operators with Nonsmooth Coefficients Iii

Denote by x = (x0, x1, ..., xn) = (x0, x′) the coordinates in R × R. Sometimes we refer to the first coordinate x0 as “time” and to x′ as “space” coordinates. The Strichartz estimates for solutions to the homogeneous wave equation in R× R, 2u = 0, u(0) = u0, ut(0) = u1, have the form ‖|D|u‖Lp(Lq) . ‖∇u0‖L2 + ‖u1‖L2. (1.1) Such an estimate holds for all pairs (ρ, p, q) satisfying the relations 2...