Related papers: An elementary formula for computing shape derivati…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…
The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…
We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial expansions of the function mapping parameter values to…
Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an…
A surface integral equation (SIE) formulation under the magneto-quasi-static assumption is proposed to efficiently and accurately model arbitrarily shaped interconnects in packages. Through decently transferring all electromagnetic…
For a semigroup $P_t$ generated by an elliptic operator on a smooth manifold $M$, we use straightforward martingale arguments to derive probabilistic formulae for $P_t(V(f))$, not involving derivatives of $f$, where $V$ is a vector field on…
We propose an integral representation for the higher-order Fr\'echet derivative of analytic matrix functions $f(A)$ which unifies known results for the first-order Fr\'echet derivative of general analytic matrix functions and for…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…
We derive integrable equations starting from autonomous mappings with a general form inspired by the multiplicative systems associated to the affine Weyl group E$_8^{(1)}$. Five such systems are obtained, three of which turn out to be…
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is…
We give a formula for matrix exponentials and partial fraction decompositions.
Studies in thermodynamics often require the reduction of some first or second order partial derivatives in terms of a smaller basic set. A simple algorithm to perform such a reduction is presented here, together with a review of earlier…
Modification of coupled integral equations method (CIEM) for calculating the characteristics of the accelerating structures is presented in this paper. In earlier developed CIEM schemes the coupled integral equations are derived for the…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.