Third-order iterative methods with applications to Hammerstein equations: A unified approach

AbstractThe geometrical interpretation of a family of higher order iterative methods for solving nonlinear scalar equations was presented in [S. Amat, S. Busquier, J.M. Gutiérrez, Geometric constructions of iterative functions to solve nonlinear equations. J. Comput. Appl. Math. 157(1) (2003) 197–205]. This family includes, as particular cases, some of the most famous third-order iterative methods: Chebyshev methods, Halley methods, super-Halley methods, C-methods and Newton-type two-step methods. The aim of the present paper is to analyze the convergence of this family for equations defined between two Banach spaces by using a technique developed in [J.A. Ezquerro, M.A. Hernández, Halley’s method for operators with unbounded second derivative. Appl. Numer. Math. 57(3) (2007) 354–360]. This technique allows us to obtain a general semilocal convergence result for these methods, where the usual conditions on the second derivative are relaxed. On the other hand, the main practical difficulty related to the classical third-order iterative methods is the evaluation of bilinear operators, typically second-order Fréchet derivatives. However, in some cases, the second derivative is easy to evaluate. A clear example is provided by the approximation of Hammerstein equations, where it is diagonal by blocks. We finish the paper by applying our methods to some nonlinear integral equations of this type

On a nonlinear subdivision scheme avoiding Gibbs oscillations and converging towards CsC^{s} functions with s>1s>1

International audienceThis paper presents a new nonlinear dyadic subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence , stability and order of approximation are analyzed. It is proved that this scheme converges towards limit functions Hölder continuous with exponent larger than 1.299. Numerical estimates provide a Hölder exponent of 2.438. This subdivision scheme is the first one that simultaneously achieves the control of the Gibbs phenomenon and has limit functions with Hölder exponent larger than 1

Super-attracting periodic orbits for a classical third order method

AbstractWe use a classical third order root-finding iterative method for approximating roots of nonlinear equations. We present a procedure for constructing polynomials so that super-attracting periodic orbits of any prescribed period occur when this method is applied. This note can be considered as the second part of our previous study [S. Amat, S. Busquier, S. Plaza, A construction of attracting periodic orbits for some classical third order iterative methods, J. Comput. Appl. Math. 189(1–2) (2006) 22–33]

Analysis and Design of Tuned Turbo Codes

It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically are asymptotically bad in the sense that their minimum distance does not grow linearly with block length, and they therefore exhibit an error floor at moderate-to-high signal to noise ratios, asymptotically good codes usually converge further away from channel capacity. In this paper, we introduce the concept of tuned turbo codes, a family of asymptotically good hybrid concatenated code ensembles, where asymptotic minimum distance growth rates, convergence thresholds, and code rates can be traded-off using two tuning parameters, {\lambda} and {\mu}. By decreasing {\lambda}, the asymptotic minimum distance growth rate is reduced in exchange for improved iterative decoding convergence behavior, while increasing {\lambda} raises the asymptotic minimum distance growth rate at the expense of worse convergence behavior, and thus the code performance can be tuned to fit the desired application. By decreasing {\mu}, a similar tuning behavior can be achieved for higher rate code ensembles.Comment: Accepted for publication in IEEE Transactions on Information Theor

On an efficient k-step iterative method for nonlinear equations

[EN] This paper is devoted to the construction and analysis of an efficient k-step iterative method for nonlinear equations. The main advantage of this method is that it does not need to evaluate any high order Frechet derivative. Moreover, all the k-step have the same matrix, in particular only one LU decomposition is required in each iteration. We study the convergence order, the efficiency and the dynamics in order to motivate the proposed family. We prove, using some recurrence relations, a semilocal convergence result in Banach spaces. Finally, a numerical application related to nonlinear conservative systems is presented. (C) 2016 Elsevier B.V. All rights reserved.This work was supported in part by the project MTM2011-28636-C02-01-{01,02} of the Spanish Ministry of Science and Innovation.Amat, S.; Bermúdez, C.; Hernández-Verón, MA.; Martínez Molada, E. (2016). On an efficient k-step iterative method for nonlinear equations. Journal of Computational and Applied Mathematics. 302:258-271. https://doi.org/10.1016/j.cam.2016.02.003S25827130

Pengembangan Bahan Ajar Matakuliah Sistem Chasis, Suspensi Dan Kemudi

Penelitian pengembangan ini menghasilkanbahan ajar matakuliah Sistem Chasis, SuspensidanKemudi yang dapat memenuhi tuntutan pencapaian: (1) kuantitas isi/materi yang optimal, dan ke‑up to date‑an informasi dalam pembelajaran; (2) kualitas prestasi akademik dan hasil sosial. Bahan ajar dirancang terdiri dari: (a) tujuankhususpembelajaran; (b) materipembelajaran yang dipelajariolehmahasiswa; (c) rangkuman; (d) soallatihan. Karakteristik yang menandai bahan ajar ini adalah adanya penataan strategi pembelajaran yang jelas dan runtut, meliputi strategi penataan isi, strategi pengelolaan dan strategi penyampaian

Model Pendidikan Karakter di SMK melalui Program Pengembangan Diri dan Kultur Sekolah

This study aimed to: (1) describe the best practices on the implementation of character education in Vocational High School models through self-development program, and (2) describe the best practices on the implementation of character education in Vocational High School models through school culture. The study was conducted through case studies at SMK N 2 Depok Sleman, SMK N 2 Wonosari, and SMK N 1 Bantul. This study employed quantitative and qualitative approaches (mix-methods). The data was collected using questionnaires, interviews, participant observation, and documentation. The data was analysed using the descriptive technique, both quantitative and qualitative. The results showed: (1) The implementation of scouting activities at SMK 2 Wonosari was intensive and very effective in instilling or developing the students\u27 positive characters, (2) The role of school culture in the character education at SMK 2 Depok Sleman focused on seven-characters values (3) The implementation of the Honesty Canteen at SMK 1 Bantul was effective to develop the value of honesty among the students

Sistem Informasi Pembayaran Spp di Smk Negeri 4 Dumai Berbasis SMS Gateway

SPP atau Sumbangan Pembinaan Pendidikan adalah sejumlah biaya yang dibebankan kepada siswa untuk membantu lembaga pendidikan memperlancar proses belajar mengajar. SPP merupakan iuran rutin sekolah yang mana pembayarannya dilakukan setiap sebulan sekali.SPP merupakan salah satu bentuk kewajiban setiap siswa yang masih aktif dilembaga tersebut. Pengelolaan informasi data pembayaran SPP Di SMK Negeri 4 Dumai saat ini masih konvensional dengan mencatat pada kartu pembayaran kemudian data pembayaran direkap pada buku.Selain itu masih kurangnya informasi dari pihak sekolah kepada orang tua atau wali siswa mengenai transaksi pembayaran dan informasi penunggakan pembayaran SPP siswa. Untuk membuat sebuah sistem yang dapat membantu proses pengolahan data administrasi pembayaran SPP di SMK Negeri 4 Dumai. Sistem informasi pembayaran SPP dibuat dengan menggunakan bahasa pemrograman PHP (Hypertext Preprocessor) serta menggunakan database MySQL dan menggunakan metode SDLC