Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods

Due to the huge amount of redundant data, the problem arises of finding a single integral solution that will satisfy numerous possible accuracy options. Mathematical processing of such measurements by traditional geodetic methods can take significant time and at the same time does not provide the required accuracy. This article discusses the application of nonlinear programming methods in the computational process for geodetic data. Thanks to the development of computer technology, a modern surveyor can solve new emerging production problems using nonlinear programming methods—preliminary computational experiments that allow evaluating the effectiveness of a particular method for solving a specific problem. The efficiency and performance comparison of various nonlinear programming methods in the course of trilateration network equalization on a plane is shown. An algorithm of the modified second-order Newton’s method is proposed, based on the use of the matrix of second partial derivatives and the Powell and the Davis–Sven–Kempy (DSK) method in the computational process. The new method makes it possible to simplify the computational process, allows the user not to calculate the preliminary values of the determined parameters with high accuracy, since the use of this method makes it possible to expand the region of convergence of the problem solution.

Comparison of Single User with Multi User Cooperative Spectrum Sensing for Energy Detector at Low SNR Wall

With rapidly increasing demand in wireless communication, available licensed spectrum resources should be utilized efficiently and actively. Cognitive radio is a device which learns from surrounding environment and transmit its signal when license spectrum is unutilized. Spectrum sensing is the need for Cognitive radio. In this paper, Energy detector is implemented though MATLAB software for single and multiusers. Region of Convergence (ROC) curve is plotted for both normal ED and Cooperative spectrum sensing ED. Results show while increasing number of samples from 1k to 100k, probability of detection is also achieved 0.9 maximum. Increasing SNR from -20dB, -15dB to -10 dB, probability of detection is improved in ROC curve. Also cooperative spectrum sensing with OR rule gives good probability of detection 0.9 to 1.

Mixed precision path tracking for polynomial homotopy continuation

This article develops a new predictor-corrector algorithm for numerical path tracking in the context of polynomial homotopy continuation. In the corrector step, it uses a newly developed Newton corrector algorithm which rejects an initial guess if it is not an approximate zero. The algorithm also uses an adaptive step size control that builds on a local understanding of the region of convergence of Newton’s method and the distance to the closest singularity following Telen, Van Barel, and Verschelde. To handle numerically challenging situations, the algorithm uses mixed precision arithmetic. The efficiency and robustness are demonstrated in several numerical examples.

Mellowness Detection of Dragon Fruit Using Deep Learning Strategy

The agriculture being a main source of income in many developing countries such as India, Indonesia, etc. The economic development of these countries depends on the GDP (Gross Domestic Progress) rate of the agricultural products. However due to miscalculations in the maturity of the fruits and vegetables leads to the wastage of foods. In general many measure were taken to minimize the food spoilage and by tracking the each stage of the vegetables and fruits carefully, but resulted in a hefty human labor, and weariness. Specifically the non-climacteric fruit such as the dragon fruit requires much attention as it is has to be harvested after it is ripened and cannot be ripened after harvesting using the hastening ripening process such as the ethylene, carbide, and CO2 etc. So the paper has put forth the application to identify the mellowness in the dragon fruit using the RESNET 152 a deep learning convolution neural network to identify the dragon fruits mellowness and it’s time to harvest. The model was trained using the python and the tensor flow. The developed structure was trained using the pictures of the dragon fruit in the different stages of its mellowness and was tested using the region of convergence and the confusion matrix with 100 new data. The testing was carried with the different number of epoch ranging from 10 to 500. The results obtained were more accurate compared to the VGG16 /19 in the terms of Accuracy and loss in training and testing.

An efficient algorithm for Padé-type approximation of the frequency response for the Helmholtz problem

We consider the map $\mathcal{S}:\mathbb{C}\to H^1_0(\Omega)=\{v\in H^1(D), v|_{\partial\Omega}=0\}$, which associates a complex value z with the weak solution of the (complex-valued) Helmholtz problem $-\Delta u-zu=f$ over $\Omega$ for some fixed $f\in L^2(\Omega)$. We show that $\mathcal{S}$ is well-defined and meromorphic in $\mathbb{C}\setminus\Lambda$, $\Lambda=\{\lambda_\alpha\}_{\alpha=1}^\infty$ being the (countable, unbounded) set of (real, non-negative) eigenvalues of the Laplace operator (restricted to $H^1_0(\Omega)$). In particular, it holds $\mathcal{S}(z)=\sum_{\alpha=1}^\infty\frac{s_\alpha}{\lambda_\alpha-z}$, where the elements of $\{s_\alpha\}_{\alpha=1}^\infty\subset H^1_0(\Omega)$ are pair-wise orthogonal with respect to the $H^1_0(\Omega)$ inner product. We define a Pad\'e-type approximant of any map as above around $z_0\in\mathbb{C}$: given some integer degrees of the numerator and denominator respectively, $M,N\in\mathbb{N}$, the exact map is approximated by a rational map $\mathcal{S}_{[M/N]}:\mathbb{C}\setminus\Lambda\to H^1_0(\Omega)$. We define such approximant within a Least-Squares framework, through the minimization of a suitable functional based on samples of the target solution map and of its derivatives at $z_0$. In particular, the denominator of the approximant is the minimizer (under some normalization constraints) of the $H^1_0(\Omega)$ norm of a Taylor coefficient of $Q\mathcal{S}$, as Q varies in the space of polynomials with degree $\leq N$. The numerator is then computed by matching as many terms as possible of the Taylor series of $\mathcal{S}$ with those of $\mathcal{S}_{[M/N]}$, analogously to the classical Pad\'e approach. The resulting approximant is shown to converge, as $M+N$ goes to infinity, to the exact map $\mathcal{S}_{[M/N]}$ in the $H^1_0(\Omega)$ norm for values of the parameter sufficiently close to $z_0$ (a sharp bound on the region of convergence is given). Moreover, it is proven that the approximate poles converge exponentially (as M goes to infinity) to the N elements of $\Lambda$ closer to $z_0$.

ON THE NUMERICAL METHOD OF CONSTRUCTION OF UNSTABLE SOLUTIONS OF DYNAMICAL SYSTEMS WITH QUADRATIC NONLINEARITIES

In this paper, the author considers the modification of the method of power series for the numerical construction of unstable solutions of systems of ordinary differential equations of chaotic type with quadratic nonlinearities in general form. A region of convergence of series is found and an algorithm for constructing approximate solutions is proposed.

Trusted frequency region of convergence for the enclosure method in thermal imaging

This study deals with the numerical implementation of a formula in the enclosure method as applied to a prototype inverse initial boundary value problem for thermal imaging in a one-space dimension. A precise error estimate of the formula is given and the effect on the discretization of the used integral of the measured data in the formula is studied. The formula requires a large frequency to converge; however, the number of time interval divisions grows exponentially as the frequency increases. Therefore, for a given number of divisions, we fixed the trusted frequency region of convergence with some given error bound. The trusted frequency region is computed theoretically using the theorems provided in this paper and is numerically implemented for various cases.