Course Information

Course Name	Turkish	Hesaplamalı Lineer Cebir
	English	Computational Linear Algebra
Course Code	MAT 263	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	1	3	3	-	-
Course Language		English
Course Coordinator		Ersin Özuğurlu
Course Objectives		1. To learn numerical solutions of linear systems, 2. To solve numerically eigenvalue-eigenvector problems, 3. To analyze convergence of iterative methods, 4. To solve linear algebra problems with popular programming languages,
Course Description		The concepts of vector and matrix norms, positive definite matrix, linear independence, dimensions and bases. Solution of linear systems: Direct methods (Gauss-Elimination, Gauss-Jordan, pivoting, Cramer methods, LU, Cholesky and QR decompositions), Iterative methods (Jacobi and Gauss-Seidel methods, Successive over relaxation method) and convergence analysis, Solutions of linear systems with popular programming languages. Eigenvalue and eigenvector problems: Gerschgorin disks, Rayleigh quotient, Trace method, Power and inverse power methods and power method with shifting. Solutions of eigenvalue-eigenvector problems with popular programming languages. Singular value decomposition.
Course Outcomes		Students completing successfully this course earns qualifications on the following subjects: I. Solutions of linear systems, II. Solutions of eigenvalue-eigenvector problems, III. Solutions of linear algebra problems with popular programming languages.
Pre-requisite(s)		MAT143/E MIN DD
Required Facilities		lab
Other		Interactive web page for Linear Algebra: http://immersivemath.com/ila/tableofcontents.html? https://ocw.mit.edu/courses/mathematics/18-086-mathematical-methods-for-engineers-ii-spring-2006/ • Notes on the Accuracy of Naive Summation (PDF) • Errors, Norms, and Condition Numbers • What Every Computer Scientist Should Know About Floating Point Arithmetic by David Goldberg. • How Java’s Floating-Point Hurts Everyone Everywhere (PDF) by William Kahan and Joseph Darcy. This article contains a nice discussion of floating-point myths and misconceptions. • Systems of Linear Equations Mathews - – Cramer's Rule – Gaussian ... • Solution Methods: Iterative Techniques Lecture 6 • Gram-Schmidt Orthogonalization (PDF) (Courtesy of Per-Olof Persson. Used with permission.) • Householder Reflectors and Givens Rotations (PDF) (Courtesy of Per-Olof Persson. Used with permission.) • : Classical vs. Modified Gram-Schmidt • The QR Algorithm I (PDF) (Courtesy of Per-Olof Persson. Used with permission.) • The QR Algorithm II (PDF) (Courtesy of Per-Olof Persson. Used with permission.) • https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/video-lectures/lecture-12-computing-eigenvalues-and-singular-values/ •
Textbook		Sewell G., Computational Methods of Linear Algebra, 3E, World Scientific, 2014.
Other References		Strang G., Introduction to Linear Algebra, Wellesley-Cambridge Press, 2016. Nassif N., Erhel J., Philippe B., Introduction to Computational Linear Algebra, CRC Press, 2016. Trefethen L. N., Bau D., III, Numerical Linear Algebra, SIAM, 1997. Lyche T., Numerical Linear Algebra and Matrix Factorizations, Springer, 2020. Demmel J. W., Applied Numerical Linear Algebra, SIAM, 1997.

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