108年第1學期-5476 矩陣計算 課程資訊
The concept of matrix computation plays an important concept in scientific computing. Especially on the topic of data science, matrix computation is the fundamental operation in machine learning and deep learning. Matrix computation, also known as numerical linear algebra, mainly consists of linear systems and eigenvalue problems. The detailed concepts of this course include basic matrix operations, matrix decomposition (e.g. LU, Cholesky, Schur form, Jordan form, QR, QZ, SVD), direct and iterative methods to solve linear systems (e.g. Gaussian elimination, Jacobi method, Gauss-Seidel, SOR, Krylov subspace methods, preconditioning) and eigenvalue problems (e.g. Arnoldi decomposition and Jacobi-Davidson method), orthogonalization and least squares problems, and some further matrix algebra as well as algorithms (matrix inverse, rank, determinant and trace).
1. Matrix Computation. Gene H. Golub and Charles F. Van Loan. Johns Hopkins University Press, 2013 (4th edition).
2. Scientific Computing with Case Studies. Dianne P. O'Leary. Society for Industrial and Applied Mathematics, 2008.