Spring 2023 (WPI): Numerical Methods for Linear and Nonlinear Systems

Office Hours

MTR 2:00 - 3:00 pm

Lecture Notes

• Lecture 1 Fundamentals of Numerical Methods
• Lecture 2 Floating-point Representation of Real Numbers
• Lecture 3 Error Analysis and Catastrophic Cancellations
• Lecture 4 Nested Polynomials and Well-conditioned Problems
• Lecture 5 Well-conditioned Problems and Stability of Algorithms
• Lecture 6 Condition Number of a Problem
• Lecture 7 Rate/Order of Convergence
• Lecture 8 Direct Methods: Gaussian Elimination with Back Substitution: Examples
• Lecture 9 Gaussian Elimination with Back Substitution: Algorithm
• Lecture 10 Gaussian Elimination with Back Substitution: Analysis
• Lecture 11 Gaussian Elimination with Partial Pivoting
• Lecture 12 LU Factorization (without Row Permutation)
• Lecture 13 PLU Factorization (with Row Permutation)
• Lecture 14 Iterative Methods, Norms of Vectors and Matrices
• Lecture 15 Cauchy-Schwarz Inequality and Examples
• Lecture 16 Equivalence of Norms; Eigenvalues and Eigenvectors
• Lecture 17 Matrix Norms and Condition Number of a Matrix
• Lecture 19 Jacobi Iteration: Algorithm
• Lecture 20 Jacobi Iteration: Convergence; Gauss-Seidel Iteration
• Lecture 21 Successive over-relaxation
• Lecture 22 Power Method for Eigenvalues
• Lecture 23 Root-finding: The Bisection Method
• Lecture 24 Root-finding: Fixed-Point Iteration
• Lecture 25 Newton's Method and Its Extensions
• Lecture 26 Fixed-Point Iteration and Newton's Method in Higher Dimensions
• Lecture 27 The Least Square Problem

Homework

• HW1
• HW2
• HW3
• HW4
• HW5
• HW6
• HW7

Exams

• Exam 1   Solutions
• Exam 2   Solutions

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