1,076 research outputs found
Creating materials with a desired refraction coefficient
A method is given for creating material with a desired refraction
coefficient. The method consists of embedding into a material with known
refraction coefficient many small particles of size . The number of
particles per unit volume around any point is prescribed, the distance between
neighboring particles is as ,
is a fixed parameter. The total number of the embedded particle is
. The physical properties of the particles are described by
the boundary impedance of the particle,
as . The refraction coefficient is the
coefficient in the wave equation
Dynamical Systems Gradient method for solving nonlinear equations with monotone operators
A version of the Dynamical Systems Gradient Method for solving ill-posed
nonlinear monotone operator equations is studied in this paper. A discrepancy
principle is proposed and justified. A numerical experiment was carried out
with the new stopping rule. Numerical experiments show that the proposed
stopping rule is efficient. Equations with monotone operators are of interest
in many applications.Comment: 2 figure
The Dynamical Systems Method for solving nonlinear equations with monotone operators
A review of the authors's results is given. Several methods are discussed for
solving nonlinear equations , where is a monotone operator in a
Hilbert space, and noisy data are given in place of the exact data. A
discrepancy principle for solving the equation is formulated and justified.
Various versions of the Dynamical Systems Method (DSM) for solving the equation
are formulated. These methods consist of a regularized Newton-type method, a
gradient-type method, and a simple iteration method. A priori and a posteriori
choices of stopping rules for these methods are proposed and justified.
Convergence of the solutions, obtained by these methods, to the minimal norm
solution to the equation is proved. Iterative schemes with a
posteriori choices of stopping rule corresponding to the proposed DSM are
formulated. Convergence of these iterative schemes to a solution to equation
is justified. New nonlinear differential inequalities are derived and
applied to a study of large-time behavior of solutions to evolution equations.
Discrete versions of these inequalities are established.Comment: 50p
Dynamical systems method for solving linear finite-rank operator equations
A version of the Dynamical Systems Method (DSM) for solving ill-conditioned
linear algebraic systems is studied in this paper. An {\it a priori} and {\it a
posteriori} stopping rules are justified. An iterative scheme is constructed
for solving ill-conditioned linear algebraic systems.Comment: 16 pages, 1 table, 1 figur
- …