Corso2020-2021 < CI

Lectures 2020-2021

Lecture 1, February 24th, 2021 Introduction to the course. Lecture 1 - Introduction

Lecture 2, February 26th, 2021 Introduction to Matlab - Part 1 - Lecture 2 - Matlab
Laboratory, February 26th, 2021 Laboratory: Introductory exercises - Part 1

Lecture 3, March 3rd, 2021 Introduction to Matlab - Part 2 - Lecture 3 - Matlab
Laboratory, March 3rd, 2021 Laboratory: Introductory exercises - Part 2

Lecture 4, March 5th, 2021 Sparse matrices: definitions and motivation of compact formats. Compact storage methods for sparse matrix: Coordinate, Skyline, Compact Sparse Row CSR, Compact Sparse Column CSC, Modified Sparse Row MSR. Lecture 4 - SparseMatrices.pdf

Appendix

of book Solving Numerical PDEs: Problems, Applications, Exercises - Formaggia, Saleri, Veneziani - 2012 - read pp. 395-409

Lecture 5, March 10th, 2021 Exercises on Sparse matrices.

Homework 1 - Sparse Matrices - Deadline: 25 March 2021

Lecture 6, March 12th, 2021 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 7 - Linear Systems Part 1

Lecture 7, March 17th, 2021 Lecture by Dr. Viviana Arrigoni. Linear systems. Cholesky factorization. Jacobi iterative method. Gauss-Seidel iterative method. Lecture 7 - Linear Systems Part 2

Homework 2 - Direct and iterative methods - Deadline: 2 April 2021

Lecture 8, March 19th, 2021 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. Uncertainty in measurements. Lecture 8 - Errors
Exercises on linear systems: Exercise 3 from Midterm exam 18 April 2018 (to be continued).

Lecture 9, March 24th, 2021 Discussion on Homework 1: student's solutions. Exercises on linear systems and errors: Exercise 3 from Midterm exam 18 April 2018 (continued); Exercise 3 from Midterm exam 17 April 2019.

Lecture 10, March 26th, 2021 Eigenvalues and eigenvectors. The Power method. The Deflation methods. 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; covariance matrix and eigenvectors. Lecture 10 - Eigenvalues, Eigenvectors and applications

Lecture 11, March 31st, 2021 Molecular Dynamics: Introduction, Hooke's Law Model, Lennard-Jones Model, Motion Equations. Lecture11 - MolecularDynamics Molecular Dynamics - L. Fosdick.

Lecture 12, April 7th, 2021 Molecular Dynamics: Euler's method and Verlet's method for Hooke's Law Model and Lennard-Jones Model. Solution of motion equations for the 1D Hard Sphere Model. Lecture12 - Molecular Dynamics Part 2 - slide 1-37 Exact solution for Hooke's Law Model. Molecular Dynamics - L. Fosdick.

Lecture 13, April 9th, 2021 Molecular dynamics: Solution of motion equations for the 1D Hard Sphere Model. Exact solution of motion equations for Hooke's Law Model. Lecture12 - Molecular Dynamics Part 2 - slide 38-65
Discussion on Homework 2: student's solutions.

Midterm test - April 16th, 2021

Lecture 15, April 23rd, 2021 Circuits for arithmetic operations. Pipeline of arithmetic operations. Circuit evaluation: delay and area. Lecture15 - Computer arithmetic

Homework3 - Eigenpairs and Molecular Dynamics - Deadline: 7 May 2021

Lecture 16, April 28th, 2021 Representations for Fast Arithmetic. Redundant number representations for carry-free addition. Modified Signed Digit (MSB) and Redundant Binary. Lecture16 - Representations for Fast Arithmetic - Slides 1-31

Lecture 17, April 30th, 2021 Representations for Fast Arithmetic: Residue number system. Lecture17 - Representations for Fast Arithmetic - Slides 32-55

Text of exercises on circuit evaluation and number representations

Lecture 18, May 5th, 2021 SIMD class: vector architecture. Lecture 18 - Vector Architectures

Lecture 19, May 7th, 2021 Graphics Processing Units. Matrix multiplication on GPUs. Lecture19 - GPUs

Lecture 20, May 12th, 2021 Interconnection networks. Lecture 20 - Interconnection networks - Slides 1 - 39

Lecture 21, May 14th, 2021 Interconnection networks: Equivalence of log N stage and (2log N -1) stage MINs; all-to-all personalized communication on log N stage and (2log N -1) stage MINs - Lecture 20 - Interconnection networks - Slides 40 - 102