Schedule

Class |
Date | Topic |
Reading |
Assigned |
Due |
---|---|---|---|---|---|

/ | Preliminaries - Scientific computing - Well-posedness - Sources of error - Absolute vs. relative error - data vs. computational error - truncation vs. rounding error
Conditioning - Stability - Forward and backward error - Stability and accuracy - Floating point general system Floating point - normalization - UFL, OFL, subnormals, rounding, machine prescision |
Heath, Chapter 1
Lecture 1 notes Lecture 2 notes Lecture 3 notes |
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/ | Homework 1 | ||||

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Floating point math - rounding error analysis - cancellation - matrix-vector multiplication - outer product - range - nullspace - rank
Solving linear systems - Existence and Uniqueness of solutions - Vector and Matrix Norms Conditioning of Ax = b - Cond(A) - Residual |
Heath, Chapter 2
Lecture 4 notes Lecture 5 notes Lecture 6 notes |
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/ | Homework 2 | Homework 1 | |||

/ | Triangular systems - Forward/Backward Substitution - LU factorization
LU - Operation Count - Instability - Pivoting LU with partial and complete pivoting - Special systems - SPD systems - Cholesky factorization |
Heath, Sections 2.4, 2.5
Lecture 7 notes Lecture 8 notes Lecture 9 notes | |||

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/ | Orthogonality - SVD
SVD and rank - Projectors Overdetermined systems - Least Squares - QR decomposition |
Heath Sections 3.1-3.6
Lecture 10 notes Lecture 11 notes Lecture 12 notes |
Homework 3 | Homework 2 | |

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Least squares and QR - Gram-Schmidt orthogonalization - Householder Reflectors - Householder QR
Practice Midterm |
Lecture 13 notes Practice Midterm and Solutions | |||

/ | Homework 3 (Friday) | ||||

/ | Midterm
Eigenvalue Problems - Power Iteration - Inverse Iteration - Rayleigh Quotient Iteration - Simultaneous Iteration Deflation - Gerschgorin's Theorem |
Heath, Sections 4.1, 4.2, 4.4, 4.5
Lecture 14 notes Lecture 15 notes Lecture 16 notes |
Homework 4 | ||

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/ | Nonlinear Equations - Root Finding - Iterative Methods - Bisection Method
Fixed Point Iteration - Newton's Method Secant Method - Safeguarded Methods - Systems of Nonlinear Euqations - Newton's Method - Secant-updating Methods |
Heath Sections 5.1-5.5.4, 5.5.7, 5.6.1-5.6.3
Lecture 17 notes Lecture 18 notes Lecture 19 notes |
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/ | Optimization - unconstrained - one-dimensional - multi-dimensional
Conditioning - Golden section search - Newton's Method - Steepest Descent Newton's Method (multi-dimensional) - Quasi-Newton Methods |
Heath Sections 6.1, 6.2.2., 6.3, 6.4.1, 6.4.3, 6.5.2-6.5.5
Lecture 20 notes Lecture 21 notes Lecture 22 notes |
Homework 5 | Homework 4 (Monday) | |

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/ | Nonlinear Conjugate Gradients - Constrained Optimality Conditions - Iterative Methods - Linear Conjugate Gradients |
Heath 6.5.6, 11.5.1-11.5.3, 11.5.5
Shewchuk 1-4, 7-8 Lecture 23 notes Lecture 24 notes Lecture 25 notes |
Homework 6 | Homework 5 | |

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/ | Practice Final
Polynomial Interpolation |
Practice Final and Solutions Lecture 26 notes |
Extra Credit | Homework 6 (Wednesday) | |

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/ | Final (Monday June 11, 8:00am-11:00am) | Extra Credit | ||

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