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Consistent Approximations of Some Geometric Differential Operators and Their Convergences
Geometric Di erential Operators Consistent discretized approximations TriangularKey words:Surface Mesh Error Analysis
2012/8/8
The numerical integration of many geometric partial di erential equations involves
discrete approximations of several first- and second-order geometric di erential operators.
In this paper, we consi...
Several Pairs of Differential Operators and Their Applications in Variational Calculusof a General Third Order Energy
Di甧rential operator Euler-Lagrange equation Complete-variation Geo-metric energy functional Curvature
2012/8/8
Gradient, divergence and Laplace-Beltrami operators over surfaces have played im-
portant roles in many 痚lds related to geometry and analysis, such as di甧rential ge-
ometry, computational geometry a...
Consistent Approximations of Some Geometric Differential Operators
Geometric Di甧rential Operators Consistent discretized approxima-tions Triangular Surface Mesh Error Analysis.
2012/8/8
The numerical integration of many geometric partial di甧rential equations in-
volve discrete approximations of some di甧rential geometric operators. In this
paper, we consider consistent discretized a...
On the Spectra and Pseudospectra of a Class of Non-Self-Adjoint Random Matrices and Operators
Pseudospectra Non-Self-Adjoint Random Matrices Operators
2011/8/22
Abstract: In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous determini...
$L^p$ and Sobolev boundedness of pseudodifferential operators with non-regular symbol: a regularisation approach
Sobolev boundedness pseudodifferential operators non-regular symbol
2010/11/11
In this paper we investigate $L^p$ and Sobolev boundedness of a certain class of pseudodifferential operators with non-regular symbols. We employ regularisation methods, namely convolution with a net ...
Compactness properties of weighted summation operators on trees - the critical case
Metrics on trees operators on trees weighted summation operators
2010/12/6
The aim of this paper is to provide upper bounds for the entropy numbers of summation
operators on trees in a critical case. In a recent paper [10] we elaborated a framework of
weighted summation op...
Some estimates for Bochner-Riesz operators on the weighted Herz-type Hardy spaces
Bochner-Riesz operators weighted Herz-type Hardy spaces Ap weights atomic decomposition
2010/12/15
In this paper, by using the atomic decomposition and molecular characterization of the homogeneous and non-homogeneous weighted Herz-type Hardy spaces H ˙K ,p q (w1,w2)(HK ,p
q (w1,w2)), we obtain s...
Approximation by certain linear operators preserving x2
Positive linear operator polynomial weighted space degree of approximation
2010/2/25
We investigate certain positive linear operators Ln preserving the functions ek (x)=xk, k=0, 1, and modified operators Ln* which preserve e0 and e2. We show that the error of approximation of f by Ln*...
Convergence Analysis of Discrete Differential Geometry Operators over Surfaces
Normal estimation Surface triangulation Convergence
2012/8/1
In this paper, we study the convergence property of several discrete schemes of the surface normal.We show that the arithmetic mean, the area-weighted averaging, and the angle-weighted averaging schem...
Convergent Discrete Laplace-Beltrami Operators over Triangular Surfaces
Laplace-Beltrami Operator Surface triangulation Discretization Convergence
2012/7/31
The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial di甧rential equations which i...
Expansions of Step-transition Operators of Multi-step Methods and Order Barriers for Dahlquist Pairs
Linear Multi-Step Method Step-Transition Operator B-series Dahlquist (Conjugate) Relation Symplecticity
2012/7/31
Using least parameters, we expand the step-transition operator of any linear multistep method (LMSM) up to O(?s+5) with order s = 1 and rewrite the expansion of the step-transition operator for s = 2 ...
On Some Properties of Szasz-Mirakyan Operators in Hölder Spaces
Szasz-Mirakyan operator Hö lder space modulus of smoothness degree of approximation
2010/3/1
We study some properties of modified Szasz-Mirakyan operators in Hölder exponential weighted spaces. We give theorems on the degree of approximation of functions by these operators.
In this paper we describe an intrinsically geometric way of producing magnetic fields on $\S^3$ and $\R^3$ for which the corresponding Dirac operators have a non-trivial kernel. In many cases we are ...