Magnetic dipole source TEM all-time apparent resistivity one-dimensional forward modeling and optimization calculation

Carrying out the forward modeling and one-dimensional apparent resistivity optimization calculation of TEM(transient electromagnetic method), theoretically verifies the the possibility that obtains the apparent resistivity in the full time domain under the condition of multiple offsets. By calculating the second derivative, Halley’s method can accelerate the iteration and make the function converge. The moment, offset and apparent resistivity are controlled by variable method. Halley’s method is used to iterate the moment, offset and apparent resistivity for completing the optimization calculation. In this paper, a conclusion will be finally drawn that the multi-offset TEM can get the apparent resistivity in the full time domain.

Comparison of Halley-Chebyshev Method with Several Nonlinear equation Solving Methods Methods

In this paper, we present one of the most important numerical analysis problems that we find in the roots of the nonlinear equation. In numerical analysis and numerical computing, there are many methods that we can approximate the roots of this equation. We present here several different methods, such as Halley's method, Chebyshev's method, Newton's method, and other new methods presented in papers and journals, and compare them. In the end, we get a good and attractive result.

CORDIC-like method for solving Kepler’s equation

Context. Many algorithms to solve Kepler’s equations require the evaluation of trigonometric or root functions. Aims. We present an algorithm to compute the eccentric anomaly and even its cosine and sine terms without usage of other transcendental functions at run-time. With slight modifications it is also applicable for the hyperbolic case. Methods. Based on the idea of CORDIC, our method requires only additions and multiplications and a short table. The table is independent of eccentricity and can be hardcoded. Its length depends on the desired precision. Results. The code is short. The convergence is linear for all mean anomalies and eccentricities e (including e = 1). As a stand-alone algorithm, single and double precision is obtained with 29 and 55 iterations, respectively. Half or two-thirds of the iterations can be saved in combination with Newton’s or Halley’s method at the cost of one division.