New Acceleration of Nearly Optimal Univariate Polynomial Root-findERS

Univariate polynomial root-finding has been studied for four millennia and is still the subject of intensive research. Hundreds of efficient algorithms for this task have been proposed. Two of them are nearly optimal. The first one, proposed in 1995, relies on recursive factorization of a polynomial, is quite involved, and has never been implemented. The second one, proposed in 2016, relies on subdivision iterations, was implemented in 2018, and promises to be practically competitive, although user's current choice for univariate polynomial root-finding is the package MPSolve, proposed in 2000, revised in 2014, and based on Ehrlich's functional iterations. By proposing and incorporating some novel techniques we significantly accelerate both subdivision and Ehrlich's iterations. Moreover our acceleration of the known subdivision root-finders is dramatic in the case of sparse input polynomials. Our techniques can be of some independent interest for the design and analysis of polynomial root-finders.Comment: 89 pages, 5 figures, 2 table

Novel Approach to Real Polynomial Root-finding and Matrix Eigen-solving

Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial has no nonreal roots, but typically nonreal roots are much more numerous than the real ones. We dramatically accelerate the known algorithms in this case by exploiting the correlation between the computations with matrices and polynomials, extending the techniques of the matrix sign iteration, and exploiting the structure of the companion matrix of the input polynomial. We extend some of the proposed techniques to the approximation of the real eigenvalues of a real nonsymmetric matrix.Comment: 17 pages, added algorithm

The identification of coupled map lattice models for autonomous cellular neural network patterns

The identification problem for spatiotemporal patterns which are generated by autonomous Cellular Neural Networks (CNN) is investigated in this paper. The application of traditional identification algorithms to these special spatiotemporal systems can produce poor models due to the inherent piecewise nonlinear structure of CNN. To solve this problem, a new type of Coupled Map Lattice model with output constraints and corresponding identification algorithms are proposed in the present study. Numerical examples show that the identified CML models have good prediction capabilities even over the long term and the main dynamics of the original patterns appears to be well represented

Model validation of spatiotemporal systems using correlation function tests

Model validation is an important and essential final step in system identification. Although model validation for nonlinear temporal systems has been extensively studied, model validation for spatiotemporal systems is still an open question. In this paper, correlation based methods, which have been successfully applied in nonlinear temporal systems are extended and enhanced to validate models of spatiotemporal systems. Examples are included to demonstrate the application of the tests

FE analysis of multi-cycle micro-forming through using closed-die upsetting models and forward extrusion models

Research in micro-forming leads to the investigation of the effects of heat generation in the workpiece and temperature changes in the tools during the forming. The results reported in this paper relate to the study of cold micro-forming processes which are usually ignored on its thermal characteristics. Two closed-die upsetting models were used for the simulation of the forming of micro-parts in single forming trial and in mass production (multi-cycle loading), respectively. An elastic-plastic finite element simulation was performed for a single forming trial. The heat transferred to the die, computed from the simulation, was then used as an input for the multi-cycle heat loading analysis in the die. Two materials: silver and low carbon steel, were used as the work material. The results show that the die saturation temperature could still go up to 100 °C for small size dies, which is significant for the forming of micro-parts. Forming errors due to the die-temperature changes were further computed, which forms a basis for developing considerations on the forming-error compensation. Using the same methods and procedures, forming of a micro-pin via forward extrusion was analysed