Penggunaan Metode Dodgson’s Condensation untuk Mencari Persamaan Karakteristik Matriks Vandermonde dan Estimasi Nilai Eigen Menggunakan Metode Newton-Raphson
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Mar 13, 2020
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Abstract
Dalam paper ini kami menyajikan penggunaan metode Dodgson’s Condensation dalam mencari persamaan karakteristik dari matriks Vandermonde dan metode Newton-Raphson untuk melakukan estimasi nilai eigen dari persamaan karakteristik matriks Vandermonde. Dengan menggunakan metode Newton-Raphson diperoleh nilai eigen dari matriks Vandermonde dengan galat yang minim.
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Fais, W., & Ulfa, F. K. (2020). Penggunaan Metode Dodgson’s Condensation untuk Mencari Persamaan Karakteristik Matriks Vandermonde dan Estimasi Nilai Eigen Menggunakan Metode Newton-Raphson. PRISMA, Prosiding Seminar Nasional Matematika, 3, 698-705. Retrieved from https://journal.unnes.ac.id/sju/prisma/article/view/37992
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References
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Yamlecha, J., Hermawan, & Handoko, S. (2012). Perbandingan Desain Optimal Power System Stabilizer (Pss) Menggunakan PSO (Particle Swarm Optimization) Dan Ga (Genetic Algorithm) Pada Single Machine Infinite Bus (SMIB). TRANSIENT, 1(4), 188–193.
Yuliani, S., Budhiati. V., R., & Mashuri. (2012). Penerapan diagonalisasi matriks dan matriks Leslie dalam memproyeksikan jumlah populasi perempuan. Unnes Journal Mathematics, 1(1), 52–59.
Aminudin, A. (2011). Analisis Eigen Sinyal Suara (Universitas Diponegoro). Retrieved from http://eprints.undip.ac.id/25725/1/ML2F302561.pdf
Anton, H., & Rorres, C. (2005). Elementary Linear Algebra (9th ed.). New Jersey: John Wiley & Sons, inc.
Chakraborty, D., Kumar Saha, S., & Al-Amin Bhuiyan, M. (2012). Face Recognition using Eigenvector and Principle Component Analysis. International Journal of Computer Applications, 50(10), 42–49.
Gilbert, F. (2001). Vandermonde matrix analysis of long-period seismograms. Geophysical Journal International, 146(3), 843–849.
Klein, A., & Spreij, P. (2003). Some Results on Vandermonde Matrices with an Application to Time Series Analysis. SIAM Journal on Matrix Analysis and Applications, 25(1), 213–223.
Kong, Q., & Zettl, A. (1996). Eigenvalues of regular Sturm-Liouville problems. Journal of Differential Equations, 131(1), 1–19.
Kunze, R., & Hoffman, K. (1971). Linear Algebra, 2Nd Edition - Kenneth Hoffmann And Ray Kunze (2nd ed.). New Jersey: Prentice Hall, inc.
Ledoux, V., Rizea, M., Van Daele, M., Vanden Berghe, G., & Silişteanu, I. (2009). Eigenvalue problem for a coupled channel Schrödinger equation with application to the description of deformed nuclear systems. Journal of Computational and Applied Mathematics, 228(1), 197–211.
Lewis, A. S. (2017). The mathematics of eigenvalue optimization. Mathematical Programming, 97(1), 155–176.
Munir, R. (2010). Metode Numerik (3rd ed.). Bandung: Penerbit Informatika.
Panda, S., & Padhy, N. P. (2008). Robust power system stabilizer design using particle swarm optimization technique. International Journal of Electrical and Computer Engineering, 2(10), 2260–2267.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes (3rd ed.). Cambridge: Cambridge University Press.
Rascon, C., & Meza, I. (2017). Localization of sound sources in robotics: A review. Robotics and Autonomous Systems, 96, 184–210.
Rice, A., & Torrence, E. (2018). “Shutting up like a telescopeâ€: Lewis Carroll’s “Curious†Condensation Method for Evaluating Determinants. The College Mathematics Journal, 38(2), 85–95.
Richard v Mises. (1964). Mathematical Theory of Probability and Statistics (1st ed.). New York: Academic Press.
Satrijo, D., Suprihanto, A., & Kholil, A. (2005). Simulasi dan analisa modus getar pada mesin Freis type vertical milling dengan menggunakan program bantu MSC Nastran. Rotasi, 7(1), 1–13.
Varberg, D., Purcell, E., & Rigdon, S. (2007). Calculus (9th ed.). Edwardsville: Pearson.
Wang, L., Horn, B. K. P., & Strang, G. (2017). Eigenvalue and Eigenvector Analysis of Stability for a Line of Traffic. Studies in Applied Mathematics, 138(1), 103–132.
Yamlecha, J., Hermawan, & Handoko, S. (2012). Perbandingan Desain Optimal Power System Stabilizer (Pss) Menggunakan PSO (Particle Swarm Optimization) Dan Ga (Genetic Algorithm) Pada Single Machine Infinite Bus (SMIB). TRANSIENT, 1(4), 188–193.
Yuliani, S., Budhiati. V., R., & Mashuri. (2012). Penerapan diagonalisasi matriks dan matriks Leslie dalam memproyeksikan jumlah populasi perempuan. Unnes Journal Mathematics, 1(1), 52–59.