Jurnal EurekaMatika
Komparasi Metode Matriks Dekomposisi Menilai Kelebihan dan Kekurangan SVD, QR, dan LU dalam Aplikasi Aljabar Linear
Abstract
Matrix decomposition techniques like Singular Value Decomposition (SVD), QR decomposition, and LU decomposition play crucial roles in various applications involving data analysis, system-solving, and data security. In this study, a comparison of the three matrix decompositions was studied. This study employs a literature review of recent research that explores the applications of SVD, QR, and LU in watermarking, encryption, and intrusion detection. The findings indicate that SVD is well-suited for applications requiring flexible computation, such as image processing and dimensionality reduction. QR excels in numerical stability and high precision for solving linear systems and cryptography; while LU is more efficient for large-scale linear system solutions. This discussion emphasizes the specific advantages of each method and its potential applications across different fields.
Keywords: Linear Algebra, LU Decomposition, Matrix Decomposition, Singular Value Decomposition, QR Decomposition.
Abstrak
Dekomposisi matriks seperti Singular Value Decomposition (SVD), Dekomposisi QR, dan Dekomposisi LU memiliki peran penting dalam berbagai aplikasi yang melibatkan analisis data, pemecahan sistem persamaan, dan pengamanan data. Pada penelitian ini dikaji perbandingan ketiga dekomposisi matriks tersebut. Metode yang digunakan adalah tinjauan literatur terhadap berbagai penelitian terkini yang mengeksplorasi aplikasi SVD, QR, dan LU dalam watermarking, enkripsi, serta deteksi intrusi. Hasil penelitian menunjukkan bahwa SVD sangat cocok untuk aplikasi yang membutuhkan komputasi fleksibel seperti pengolahan citra dan pengurangan dimensi, QR unggul dalam stabilitas numerik dan presisi tinggi untuk pemecahan sistem persamaan linear dan kriptografi, sedangkan LU lebih efisien dalam penyelesaian sistem persamaan linear besar. Pembahasan ini menekankan keunggulan spesifik masing-masing metode dan aplikasi potensialnya di berbagai bidang.
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DOI: https://doi.org/10.17509/jem.v12i2.75857
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