69,727 research outputs found
Algorithms based on DQM with new sets of base functions for solving parabolic partial differential equations in dimension
This paper deals with the numerical computations of two space dimensional
time dependent parabolic partial differential equations by adopting adopting an
optimal five stage fourth-order strong stability preserving Runge Kutta
(SSP-RK54) scheme for time discretization, and three methods of differential
quadrature with different sets of modified B-splines as base functions, for
space discretization: namely i) mECDQM: (DQM with modified extended cubic
B-splines); ii) mExp-DQM: DQM with modified exponential cubic B-splines, and
iii) MTB-DQM: DQM with modified trigonometric cubic B-splines. Specially, we
implement these methods on convection-diffusion equation to convert them into a
system of first order ordinary differential equations,in time which can be
solved using any time integration method, while we prefer SSP-RK54 scheme. All
the three methods are found stable for two space convection-diffusion equation
by employing matrix stability analysis method. The accuracy and validity of the
methods are confirmed by three test problems of two dimensional
convection-diffusion equation, which shows that the proposed approximate
solutions by any of the method are in good agreement with the exact solutions
Redundancy Allocation of Partitioned Linear Block Codes
Most memories suffer from both permanent defects and intermittent random
errors. The partitioned linear block codes (PLBC) were proposed by Heegard to
efficiently mask stuck-at defects and correct random errors. The PLBC have two
separate redundancy parts for defects and random errors. In this paper, we
investigate the allocation of redundancy between these two parts. The optimal
redundancy allocation will be investigated using simulations and the simulation
results show that the PLBC can significantly reduce the probability of decoding
failure in memory with defects. In addition, we will derive the upper bound on
the probability of decoding failure of PLBC and estimate the optimal redundancy
allocation using this upper bound. The estimated redundancy allocation matches
the optimal redundancy allocation well.Comment: 5 pages, 2 figures, to appear in IEEE International Symposium on
Information Theory (ISIT), Jul. 201
Approximation of Entropy Numbers
The purpose of this article is to develop a technique to estimate certain
bounds for entropy numbers of diagonal operator on spaces of p-summable
sequences for finite p greater than 1. The approximation method we develop in
this direction works for a very general class of operators between Banach
spaces, in particular reflexive spaces. As a consequence of this technique we
also obtain that the entropy number of a bounded linear operator T between two
separable Hilbert spaces is equal to the entropy number of the adjoint of T.
This gives a complete answer to the question posed by B. Carl [4] in the
setting of separable Hilbert spaces.Comment: 10 page
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