The radiosity equation occurs in computer graphics, and its solution leads to more realistic illumination for the display of surfaces. We consider the behavior of the radiosity integral operator, for smooth and piecewise smooth surfaces. A collocation method for solving the radiosity equation is proposed and analyzed. The method uses piecewise linear interpolation; and for one particular choice...

in this article, we will estimate efficiency amountof decision-making unit by offering the continuous piecewise polynomialextrapolation and interpolation by ccr model input-oriented on the assumptionthat it is constant returns to scale in different times. and finally, we willestimate efficiency amount of decision-making unit indifferent times byoffering an example.

<p style='text-indent:20px;'>Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects regularity (coefficients the) linearized system and, in turn, effectiveness assessing local stability by approximating Floquet multipliers. To overcome problem when computing mult...

In this paper we give necessary and sufficient conditions for convergence of continuous collocation approximations of solutions of first kind Volterra integral equations. The results close some longstanding gaps in the theory of polynomial spline collocation methods for such equations. The convergence analysis is based on a Runge-Kutta or ODE approach.

Here we propose a new method based on projections for the approximate solution of eigenvalue problems. For an integral operator with a smooth kernel, using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomials of degree ≤ r−1, we show that the proposed method exhibits an error of the order of 4r for eigenvalue approximation and of the order of 3r fo...

Abstract Settlements severely affect historic masonry arch bridges worldwide. There are countless examples of structural dislocations and ruins in recent years due to severe settlements at the base pier foundations, often caused by shipworm infestation wooden foundations or scouring riverbed erosion phenomena. The present paper proposes an original way approach failure analysis settled bridges....