Metode Ruang Bagian Krylov dan Aplikasinya pada Persamaan Matriks Gabungan Umum

Faqih Wahyu Majid, Prof. Dr. Sri Wahyuni, S.U.

2023 | Skripsi | MATEMATIKA

Pada skripsi ini dibahas metode ruang bagian Krylov dan aplikasinya pada persamaan matriks gabungan umum. Metode ruang bagian Krylov adalah keluarga algoritma untuk menyelesaikan sistem linier berukuran besar yang mencari solusi pendekatan dari suatu ruang bagian Krylov yang diberikan. Namun metode ruang bagian Krylov adalah metode iteratif, bukan algoritma langsung, dan biasanya membutuhkan perkalian (product) matriks-vektor cepat untuk A. Ada banyak metode pada ruang bagian Krylov, dalam skripsi ini digunakan metode FOM dan metode GMRES untuk menyelesaikan masalah pada persamaan matriks gabungan umum.

In this undergraduate thesis it will be discussed theKrylov subspace methods and its application on general coupled matrix equations. The Krylov subspace methods are a family of algorithms for solving a large linear systems that search for an approximate solution from a Krylov subspaces. However, the Krylov subspace methods are iterative method, as opposed to direct, algorithms and usually require a fast matrix-vector product for A. There are many methods in the Krylov subspace, in this undergraduate thesis the FOM method and the GMRES method are used to solve problems on general coupled matrix equation In this undergraduate thesis it will be discussed theKrylov subspace methods and its application on general coupled matrix equations. The Krylov subspace methods are a family of algorithms for solving a large linear systems that search for an approximate solution from a Krylov subspaces. However, the Krylov subspace methods are iterative method, as opposed to direct, algorithms and usually require a fast matrix-vector product for A. There are many methods in the Krylov subspace, in this undergraduate thesis the FOM method and the GMRES method are used to solve problems on general coupled matrix equations.

Kata Kunci : Metode Ruang Bagian Krylov, Algoritma Arnoldi, FOM, GMRES, Persamaan Matriks Gabungan Umum