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In this paper, the variations of both subunitary polar factors and Hermitian positive semidefinite polar factors in the polar decomposition are studied. New perturbation bounds of both polar factors are given without the restriction that A and its perturbed matrix à have the same rank. These improve recent results.
This article deals with a local improvement of domain decomposition methods for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents conical singularities. The problem amounts to determining the coefficients of interface boundary conditions so that the domain decomposition algorithm has rapid convergence. Specific problems occur in the presence of conical...
The aim of this paper is to study the behavior of the operators Tλ defined by $$ T_\lambda (f;x) = \int\limits_a^b {K_\lambda (t - x,f(t))dt,x \in < a,b > .} $$ . Here we estimate the rate of convergence at a point x, which has a discontinuity of the first kind as λ → λ0. This study is an extension of the papers [9] and [13], which includes Bernstein operators. Beta operators, Picard...
We present an extension theorem for polynomial functions that proves a quasi-optimal bound for a lifting from L2 on edges onto a fractional-order Sobolev space on triangles. The extension is such that it can be further extended continuously by zero within the trace space of H1. Such an extension result is critical for the analysis of non-overlapping domain decomposition techniques applied to the...
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