Konrad Zuse built the machine Z3 from 1939 to 1941 in the Methfesselstraße 7 in BerlinKreuzberg with some friends and a small support by the government. With the Z3 Konrad Zuse wanted to show, that it is possible to build a reliable working machine for very complicated arithmetic calculations, which is freely programmable and is based on a binary floating point number and switching system. For ...

It is well known that having 3 temporal phase shifting (PS) interferograms we do not have many possibilities of using an algorithm with a desired frequency spectrum, detuning, and harmonic robustness. This imposes severe restrictions on the possibilities to demodulate such set of temporal interferograms. It would be nice to apply for example a 7 step PS algorithm to these 3 images in order to h...

We have implemented in Matlab a Gauss-like cubature formula over bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n− 1 using N ∼ cmn nodes, 1 ≤ c ≤ p, m being the total number of points given on the boundary. It does not need any decomposition of the domain,...

We have implemented in Matlab a Gauss-like cubature formula over arbitrary bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n− 1 using N ∼ cmn2 nodes, 1 ≤ c ≤ p, m being the total number of points given on the boundary. It does not need any decomposition of ...

The Gauss-Kronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software libraries. For a long time, very little was known about the error of the Gauss-Kronrod scheme. An essential progress was made only recently, based on new bounds and as-ymptotic properties for the S...

In this paper we give some new results in extremal problems with polynomials which are generalization of some results of F. Locher. 2000 Mathematical Subject Classification: 26D15, 65D32 In [6] F. Locher studies some extremal problems for semidefinition polynomials (nenegative or nepositive) with the dominant coefficient equal to 1. For this he uses the quadrature formulae with high algebraical...

We introduce a finite class of weighted quadrature rules with the weight function |x|−2a exp −1/x2 on −∞,∞ as ∫−∞|x|−2a exp −1/x2 f x dx ∑n i 1 wif xi Rn f , where xi are the zeros of polynomials orthogonal with respect to the introduced weight function, wi are the corresponding coefficients, andRn f is the error value. We show that the above formula is valid only for the finite values of n. In...