Homework 1: Discussion on exercises of and laboratory. Homework 1 -Sparse Matrices - Deadline: 22 March 2020
Lecture 6, March 11th, 2020 Lecture by Dr. Viviana Arrigoni. Linear systems. Gaussian elimination for solving systems of linear equations. Pivoting. Methods to avoid pivoting. Random Butterfly Transformations and Transpose methods Lecture 6 - Linear Systems Part 1Lecture 7, March 16th, 2020 Lecture by Dr. Viviana Arrigoni. Linear systems. Cholesky factorization. Jacobi iterative method. Gauss-Seidel iterative method. Lecture 7 - Linear Systems Part 2 Lecture 8, March 18th, 2020 Errors: Computational errors, Data errors, Truncation errors, Rounding errors. Forward error and backward error. Sensitivity and condition number. Stability and accuracy. Errors in floating-point representation. Lecture 8 - Errors - Slides 1-55
Lecture 9, March 23th, 2020 Errors in floating point arithmetic. Uncertainty in measurements. Lecture 9 - Errors - Slides 56-84 Laboratory Discussion on Homework 1: solutions of students. Lecture 10, March 25th, 2020 Eigenvalues and eigenvectors. The Power method. The Deflation methods. Lecture 10 - Eigenvalues, Eigenvectors - Slides 1-30 Lecture 11, March 30th, 2020 Applications: Gould Index - Eigenvector Centrality in a Graph; the Fiedler Eigenvector and the Graph Partitioning; the Steady State of a Markov Chain using Eigenvalues and Eigenvectors. Lecture 11 - Eigenvalues, Eigenvectors - Slides 31-59
Exercises on sparse matrices and errors: Exercise 1 and Exercise 3 from Midterm test 17 April 2019, Exercise 1 from Endterm test 31 May 2016. Lecture 12, April 1st, 2020 Exercises on Jacobi and Gauss-Seidel methods and Cholesky factorization - Exercise 2 and 3 from Midterm test 18 April 2018, Power method Exercise 5 from Exam test 15 July 2019.