Abstract: In this paper, we present two new one-step iterative
methods based on Thiele-s continued fraction for solving nonlinear
equations. By applying the truncated Thiele-s continued fraction
twice, the iterative methods are obtained respectively. Analysis of
convergence shows that the new methods are fourth-order convergent.
Numerical tests verifying the theory are given and based on the
methods, two new one-step iterations are developed.
Abstract: In the present paper, we present a modification of the
New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari
[J. Math. Anal. Appl. 2006;316:753–763] and use it for solving
systems of nonlinear functional equations. This modification yields
a series with faster convergence. Illustrative examples are presented
to demonstrate the method.
Abstract: The decoding of Low-Density Parity-Check (LDPC) codes is operated over a redundant structure known as the bipartite graph, meaning that the full set of bit nodes is not absolutely necessary for decoder convergence. In 2008, Soyjaudah and Catherine designed a recovery algorithm for LDPC codes based on this assumption and showed that the error-correcting performance of their codes outperformed conventional LDPC Codes. In this work, the use of the recovery algorithm is further explored to test the performance of LDPC codes while the number of iterations is progressively increased. For experiments conducted with small blocklengths of up to 800 bits and number of iterations of up to 2000, the results interestingly demonstrate that contrary to conventional wisdom, the error-correcting performance keeps increasing with increasing number of iterations.
Abstract: This paper describes simple implementation of
homotopy (also called continuation) algorithm for determining the proper resistance of the resistor to dissipate energy at a specified rate of an electric circuit. Homotopy algorithm can be considered as a developing of the classical methods in numerical computing such as Newton-Raphson and fixed
point methods. In homoptopy methods, an embedding
parameter is used to control the convergence. The method purposed in this work utilizes a special homotopy called Newton homotopy. Numerical example solved in MATLAB is given to show the effectiveness of the purposed method