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Asmara Karma
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Mathematics

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METODE GAUSS-SEIDEL PREKONDISI DENGAN MENGGUNAKAN EKSPANSI NEUMANN Adrika, Juanita; ', Syamsudhuha; Karma, Asmara
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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Abstract

We discuss a preconditioned Gauss-Seidel method to solve a system of linear equation Ax = b by A which is a strictly diagonally dominant Z-matrix. Preconditioning matrix to be used is P = (I +U) −1 , where I is an identity matrix and U is a strictly upper triangular matrix. Using Neumann’s expansion to approximate P, we showthat the preconditioning matrix is equivalent to an existing preconditioning matrix of the form P = (I + βU). Numerical computations show that the proposed preconditionedGauss-Seidel method is better than the standard Gauss-Seidel method in solving a system of linear equation Ax = b.
KONSTRUKSI SEDERHANA METODE ITERASI BARU ORDE TIGA Dedi Mangampu Tua; Syamsudhuha '; Asmara Karma
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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We discuss two modications of Newton's methods for solving a nonlinear equation, constructed from two known third-order iterative methods. Our approach is to approximate a derivative from the improvement of the two known third-order iterative methods. Analytically it is shown that each modication of Newton's methodhas third order of convergence, and it requires three function evaluations per iteration. Therefore, its eciency index is 1:414, which is the same as Newton's method. Numerical examples show both methods are competitive with known third-order methods.
METODE BERTIPE STEFFENSEN DENGAN ORDE KONVERGENSI OPTIMAL UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR Sarbaini '; Imran M.; Asmara Karma
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses a mo dification of a third order Steffensen-typ e method, by adding three different weight functions into the third order Steffensen-type method, so that we obtain three different correction Steffensen-typ e metho ds. These methods are of order three and require three function evaluations p er iteration so that their index of efficiency is 1.587. Computational results show the correction Steffensentype methods are competitive enough in their class.
METODE BERTIPE NEWTON UNTUK AKAR GANDA DENGAN KONVERGENSI KUBIK Risvi Ayu Imtihana; Imran M.; Asmara Karma
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses a Newton-type method for multiple roots, which is derived using a linear combination of Newton’s method for multiple roots and an iterative method derived based on a quadrature Gauss-type. Analytic studies show that this iterative method has a third order of convergence and for each iteration, it requires function evaluations three times, so that the efficiency index of the method is 1.44225. Furthermore, computational tests show that the method is superior to other mentioned methods, in terms of the number of iterations required to obtain the roots.
SOLUSI POLINOMIALPERSAMAAN HERMITE YANG DIPERUMUM Suriyaamsah '; Asmara Karma; Aziskhan '
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses how to find a solution of generalized Hermite equation in the form of a polynomial. The discussion focuses on a necessary and sufficient condition for the existence of polynomial solutions of the generalized Hermite equation. By providing certain restrictionson the coefficients of the polynomial, the solution obtained is a monic polynomial.
METODE RELAKSASI NEWTON DAN KELAKUAN DINAMIKNYA Yuniza '; Leli Deswita; Asmara Karma
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
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Abstract

We discuss a relaxation of Newton method, obtained by introducing a functioncomposed of the original function in an existing problem and its derivative. This methods consists of two parameters. Certain values of the parameters give several known iterative methods. Using Taylor expansion, we show that the method is of order two. We compare the relaxation of Newton method with other known existing methods using some test functions by looking at the number of the methods obtaining the roots of the problem and using Basins of Attraction.
Co-Authors Aziskhan ' Cecep Kusmana Dedi Mangampu Tua Imran M. Juanita Adrika Leli Deswita Risvi Ayu Imtihana Sarbaini Sarbaini Suriyaamsah ' Yuniza '