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Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...
Graph filters, defined as polynomial functions of a graph-shift operator (GSO), play a key role in signal processing over graphs. In this work, we are interested in the adaptive and distributed estimation of graph filter coefficients from streaming graph s ...
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh; those attached to ...
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...
This thesis evaluates the effects of the position of the concrete core and its stiffness on the horizontal deformation of a multi-storey timber-concrete hybrid building. As part of the evaluation a calculation method with polynomial functions was derived t ...
Pressurised water supply systems are infrastructures that offer a potential for energy recovery in locations where these systems operate with an excessive pressure. The integration of micro hydropower plants for energy recovery is a challenge, as these sys ...
This work focuses on the development of a non-conforming method for the coupling of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a finite number of Lagrange multipliers defined over the interfac ...
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of ...
The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...
2020
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We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial trans ...
