John B. Kioustelidis

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A well known theorem by Bolzano states that, whenever a continuous real function changes sign in some interval, it must have a zero in this interval. Then-dimensional generalisation of this theorem, due to C. Miranda, is used for the construction of an error estimation procedure for approximate solutions of nonlinear systems of equations. Ein bekannter Satz(More)
The L1 approximation of strictly convex functions by means of first degree splines with a fixed number of knots is studied. The main theoretical results are a system of equations for the knots, which solves the problem, and an estimate of the approximation error. The error estimation allows the determination of bounds for the number of knots needed so that(More)
Segmented approximations with free knots for a given continuous function are discussed in a general form. This form includes any kind of continuous approximating segments, and a great variety of error criteria, such as anyL s -norm, or the maximum norm of the pointwise error. It is shown that a solution to the problem exists under very general conditions,(More)
A new error bound for any approximate solutionu of the two-point boundary value problemAy:=−(py′)′+qy=f,y(0)=0, y(1)=0, is proposed. This error bound depends on the deviationAu−fjust like the one which is proportional to ‖Au−f‖2, but in the case of Ritz-Galerkin approximations by cubic splines it behaves asymptotically likeh 3, whereh is the knot distance,(More)
New a posteriori (computable) upper bounds for theL 2-norms, both ofD(u−v) and ofu−v are proposed, whereu is the exact solution of the boundary value problem $$Au: = - D(pDu) + qu = f, x \in G and u = 0,x \in \partial G$$ andv any approximation of it (D is here the vector of partial derivatives with respect to the components ofx). It is shown that the new(More)
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