This paper describes a study of a class of algorithms for the floating-point divide and square root operations, based on the Newton-Raphson iterative method. The two main goals were: (1) Proving the IEEE correctness of these iterative floating-point algorithms, i.e. compliance with the IEEE-754 standard for binary floating-point operations [1]. The focus was on software driven iterative algorit...

Using the bisection as well as the Newton-Raphson method, we compute to high precision the Littlewood-Salem-Izumi constant frequently occurring in the theory of trigonometric sums.

Three multiplicative algorithms for the floatingpoint divide operation are compared: the Newton-Raphson method, Goldschmidt’s algorithm, and a naive method that simply calculates a form of the Taylor series expansion of a reciprocal. The series also provides a theoretical basis for Goldschmidt’s algorithm. It is well known that, of the Newton-Raphson method and Goldschmidt’s algorithm, the form...

Steady state analysis of a 3-φ SEIG is generally done through mathematical modeling of its equivalent circuit. The impedance model can be reduced in terms of two nonlinear simultaneous equations consisting of unspecified variables as magnetizing reactance Xm and generated frequency F. The steady state performance analysis of SEIG becomes uncomplicated once the values of Xm and F are explicitly ...

This paper proposes a parallel solver for the nonlinear systems in Bernstein form based on subdivision and the Newton-Raphson method, where the Kantorovich theorem is employed to identify the existence of a unique root and guarantee convergence of the Newton-Raphson iterations. Since the Kantorovich theorem accommodates a singular Jacobian at the root, the proposed algorithm performs well in a ...

A Modern wireless broadband system of MIMO OFDM (multiple input multiple output orthogonal frequency division multiplexing) is more popular because of good data transmission rate, robustness against multipath fading and better spectral efficiency. This system provides reliable communication and wider coverage. A main challenge to MIMO OFDM system is the retrieval of channel state information (C...

This paper presents an efficient method for solving the direct kinematics of parallel manipulators that follow a defined singularity-free trajectory. Despite the main problem is to solve the inverse kinematics, calculating the errors between the desired path and the actual path requires solving the forward kinematics which is a challenging problem. The proposed method combines closed-loop Jacob...

Restricted Maximum Likelihood estimation using first and second derivatives of the likelihood is described. It relies on the calculation of derivatives without the need for large matrix inversion using an automatic differentiation procedure. In essence, this is an extension of the Cholesky factorisation of a matrix. A reparameterisation is used to transform the constrained optimisation problem ...

In this report, we develop a procedure to analyze the relationship between the observed multi-dimensional counts and a set of explanatory variables. The counts follow a multivariate Poisson distribution or a multivariate zero-inflated Poisson distribution. Maximum likelihood estimates (MLE) for the model parameters are obtained by the Newton-Raphson (NR) iteration and the expectation-maximizati...

Ventilation is one of the key safety tasks in underground mines. Determination of the airflow through mine openings and ducts is complex and often requires the application of numerical analysis. The governing equations used in the computation of mine ventilation are discussed in matrix forms. The aim of this paper is to compare the most frequently used numerical analysis methods, which includes...