| Class | Date | Topic | Reading | Assigned | Due |
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| / | Preliminaries - Scientific computing - Well-posedness - Sources of error - Absolute vs. relative error - data vs. computational error - truncation vs. rounding error |
Heath, Chapter 1
Lecture 1 notes |
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Conditioning - Stability - Forward and backward error - Stability and accuracy - Floating point general system
Floating point - normalization - UFL, OFL, subnormals, rounding, machine prescision Floating point math - rounding error analysis - cancellation - matrix-vector multiplication - outer product - range - nullspace - rank |
Heath, Chapter 1
Lecture 2 notes Lecture 3 notes Lecture 4 notes |
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Solving linear systems - Existence and Uniqueness of solutions - Vector and Matrix Norms
Conditioning of Ax = b - Cond(A) - Residual Triangular systems - Forward/Backward Substitution - LU factorization |
Heath, Chapter 2
Lecture 5 notes Lecture 6 notes Lecture 7 notes | |||
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LU - Operation Count - Instability - Pivoting
LU with partial and complete pivoting - Special systems - SPD systems - Cholesky factorization Orthogonality - SVD | Heath Sections 3.1-3.6
Lecture 8 notes Lecture 9 notes Lecture 10 notes |
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SVD and rank - Projectors
Practice Midterm Midterm |
Lecture 11 notes
Practice Exam and Solutions | |||
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Monday - NO CLASS
Overdetermined systems - Least Squares - QR decomposition Least squares and QR - Gram-Schmidt orthogonalization - Householder Reflectors - Householder QR |
Lecture 12 notes Lecture 13 notes |
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| / | Eigenvalue Problems - Power Iteration - Inverse Iteration
Rayleigh Quotient Iteration - Simultaneous Iteration |
Heath, Sections 4.1, 4.2, 4.4, 4.5
Lecture 14 notes Lecture 15 notes |
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| - | / | Monday - HOLIDAY
Nonlinear Equations - Root Finding - Iterative Methods - Bisection Method Fixed Point Iteration - Newton's Method |
Heath Sections 5.1-5.5.4, 5.5.7, 5.6.1-5.6.3
Lecture 17 notes Lecture 18 notes |
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Secant Method - Safeguarded Methods - Systems of Nonlinear Equations - Newton's Method - Secant-updating Methods
Optimization - unconstrained - one-dimensional - multi-dimensional Friday - HOLIDAY |
Heath Sections 6.1, 6.2.2., 6.3, 6.4.1, 6.4.3, 6.5.2-6.5.5
Lecture 19 notes Lecture 20 notes |
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Conditioning - Golden section search - Newton's Method - Steepest Descent
Newton's Method (multi-dimensional) - Quasi-Newton Methods |
Heath 6.5.6, 11.5.1-11.5.3, 11.5.5
Lecture 21 notes Lecture 22 notes Lecture 23 notes |
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| / | Constrained Optimality Conditions
Iterative Methods - Conjugate Gradients Method Practice Final |
Shewchuk 1-4, 7-8
Practice Final and Solutions Problem 23 Problem 24 More practice problems with solutions |
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| - | / | Final (Monday December 10, 8:00am-11:00am) |