The most popular method for computing the matrix logarithm is a combination of inverse scaling and squaring in conjunction with Padé approximation, sometimes accompanied by Schur decomposition. In this work, we present Taylor series algorithm, based on free-transformation approach technique, that uses recent polynomial formulas evaluating approximation more efficiently than Paterson–Stockmeyer ...

Simulating the dynamics of many-body quantum systems is believed to be one first fields that computers can show a advantage over classical computers. Noisy intermediate-scale (NISQ) algorithms aim at effectively using currently available hardware. For simulation, various types NISQ have been proposed with individual advantages as well challenges. In this work, we propose new algorithm, truncate...

In this paper a computational algorithm for nonlinear balanced realization and model reduction based on Taylor series expansion is proposed. This algorithm requires recursive computations with respect to the order of the Taylor series in which we need to solve linear equations with unknown parameters in each step. Furthermore, the proposed method is applied to a double pendulum system. Some num...

In algorithms of nonlinear Kalman filter, the so-called extended Kalman filter algorithm actually uses first-order Taylor expansion approach to transform a nonlinear system into a linear system. It is obvious that this algorithm will bring some systematic deviations because of ignoring nonlinearity of the system. This paper presents two extended Kalman filter algorithms for nonlinear systems, c...

The rapid development of today’s society and the rapidly increasing incidence skeletal injuries caused by traffic industrial accidents have led to a significant increase in number patients with fractures accompanied severe soft tissue injuries, as well an increased osteomyelitis bone defects. Many these cannot be treated internal fixators can only external fixators. Taylor Bone External Fixator...

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

Abstract— This paper presents a novel approach to obtain fast locking PLL by embedding a nonlinear element in the loop of PLL. The nonlinear element has a general parametric Taylor expansion. Using genetic algorithm (GA) we try to optimize the nonlinear element parameters. Embedding optimized nonlinear element in the loop shows enhancements in speed and stability of PLL. To evaluate the perform...

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