This lecture will show by example some of the problems that occur when the roots of a polynomial are computed using a standard polynomial root solver. In particular, polynomials of high degree with a large number of multiple roots will be considered, and it will be shown that even roundoff error due to floating point arithmetic, in the absence of data errors, is sufficient to cause totally inco...

The natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first order logic program with default negation. In a preliminary step this program with variables is translated in an equivalent propositional one by a first tool: the grounder. Then, the propositional program is given to a second tool: the...

In this paper, we report a nonlinear 3D image reconstruction algorithm featuring 3D finite element forward modeling with an iterative multi-right-hand-side solver and an automatic mesh generation technique for efficient geometry modeling. The forward mesh was generated based on 3D tomosynthesis images acquired simultaneously with optical measurements. An efficient iterative solver based on a QM...

We develop a numerical method for solving shape optimization of functionals involving Steklov eigenvalues and apply it to the problem maximization k-th eigenvalue, under volume constraint. A similar study in planar case was already addressed literature using boundary integral equation method. Here we extend that 3D 4D cases, Method Fundamental Solutions as forward solver.

A numerical simulation method of computational fluid dynamics (CFD) coupling with a trim analysis for coaxial rotor systems is described in this paper. The implemented using rotorcraft flow solver, rFlow3D. Six target forces and moments, which are the thrust system, rolling pitching moments each upper lower rotor, torque balance yaw control, considered as conditions. blade pitch angles both rot...

Electrical impedance tomography (EIT) consists in probing biological tissues with low amplitude alternating electrical fields through surface electrodes, and analyzing the response of the medium to reconstruct its electrical characteristics. EIT has been considered for a wide range of clinical applications, the most promising being continuous pulmonary function monitoring. In the EIT reconstruc...

In the present paper, we introduce a variant of numerical scheme called deep solver PDE. Our is based on non-linear version discrete-time Clark--Ocone formula, which describes convergent expansion error terms. new incorporates higher-order terms, conjecture to stabilize stochastic gradient descent procedure, and also irregularities in driver terminal function associated forward-backward differe...

solving a large sparse set of linear equations is of the problems widely seen in every numerical investigation in the entire range of engineering disciplines. employing a finite element approach in solving partial derivative equations, the resulting stiffness matrices would contain many zero-valued elements. moreover, storing all these sparse matrices in a computer memory would slower the compu...

We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Equations with terminal conditions that time-steps the BSDE backwards and apply it to differential rates problem as prototypical nonlinear of independent financial interest. The equation backward time-step is solved exactly or by Taylor-based approximation. This first application such time-stepping ap...