Abstract A new method to enclose the pseudospectrum via numerical range of inverse a matrix or linear operator is presented. The applied finite-dimensional discretizations an on infinite-dimensional Hilbert space, and convergence results for different approximation schemes are obtained, including finite element methods. We show that full contained in intersection sets which expressed terms rang...

The algorithmic differentiation in the COCONUT Environment does not only provide point evaluations but also range enclosures of derivatives up to order 3, as well as slopes up to second order. Care is taken to ensure that rounding errors are treated correctly. The ranges of the enclosures can be tightened by combining the evaluation routines with constraint propagation. Advantages and pitfalls ...

In this paper, natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function (RBF). The nanofluids used were Cu-water or -water mixture with nanoparticle volume fractions range of . A system continuity, momentum, energy partial differential equations in modeling the flow temperature behavior fluids....

An enclosure of a composite spline surface is a pair of simpler approximations that sandwich the surface. In particular, we are interested in efficiently constructing two triangulations, so that matched triangle pairs enclose a piece of the curved surface. The width of the enclosure, i,e. the distance between inner and outer hull, can be easily measured, because it is taken on at a vertex. Encl...

This paper serves as background information for the Vienna proposal for interval standardization, explaining what is needed in practice to make competent use of the interval arithmetic provided by an implementation of the standard to be. Discussed are methods to improve the quality of interval enclosures of the range of a function over a box, considerations of possible hardware support facilita...

We investigated the functional response of the least weasel (Mustela ni6alis ni6alis) in a series of experiments conducted in large outdoor enclosures (0.5 ha). Radiocollared Microtus voles were released in the enclosures at different densities (4, 8, 16 and 100/ha) three days before the release of a radiocollared weasel. During the three-day experiment every vole killed was replaced with anoth...

Interval Newton methods are widely used to find reliable enclosures for the roots of the polynomial systems. But the computation process needs the evaluation of an enclosure for the derivative of the polynomial and evaluation of the polynomial at a particular point. Again, the subdivisions (if any are needed) will require repeated evaluation of the function values. We propose an alternative app...