This resource index gives users access to most of the course resources in a single location.
LecTURES
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LECTURE HANDOUTS & ACCOMPANYING NOTEBOOKS
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PROBLEM SETS/EXAM AND SOLUTIONS
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Lecture 1: Course Overview, Newton's Method for Root-Finding
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Square Roots via Newton's Method (PDF)
Square Roots
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Problem Set 1 (PDF)
Problem set 1 notebook
Solutions to Problem Set 1 (PDF)
Solutions to Problem Set 1 notebook
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Lecture 2: Floating-Point Arithmetic
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Floating-Point Arithmetic, the IEEE Standard (PDF) (Courtesy of Per-Olof Persson. Used with permission.)
Floating-Point Arithmetic
Some Myths about Floating-Point Arithmetic (PDF)
Julia & IJulia Cheat-Sheet (PDF)
Introduction to Julia (PDF)
Julia for Numerical Computation in MIT Courses
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[No problem set]
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Lecture 3: Floating-Point Summation and Backwards Stability
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Notes on the Accuracy of Naive Summation (PDF)
Backwards Stability of Recursive Summation (PDF)
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[No problem set]
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Lecture 4: Norms on Vector Spaces
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Notes on the Equivalence of Norms (PDF)
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[No problem set]
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Lecture 5: Condition Numbers
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[No handout/notebook]
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Problem set 2 (PDF)
Solutions to Problem Set 2 (PDF)
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Lecture 6: Numerical Methods for Ordinary Differential Equations
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Modern Differential Equations Solver Software: Where We Are and Where We're Headed (PDF - 2.4MB) (Courtesy of Christopher Rackauckas. Used with permission.)
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[No problem set]
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Lecture 7: The SVD, its Applications, and Condition Numbers
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[No handout/notebook]
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[No problem set]
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Lecture 8: Linear Regression and the Generalized SVD
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Many Viewpoints on Linear Regression
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[No problem set]
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Lecture 9: Solving the Normal Equations by QR and Gram-Schmidt
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[No handout/notebook]
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[No problem set]
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Lecture 10: Modified Gram-Schmidt and Householder QR
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Householder Reflectors and Givens Rotations (PDF) (Courtesy of Per-Olof Persson. Used with permission.)
Classical vs. Modified Gram-Schmidt
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[No problem set]
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Lecture 11: Matrix Operations, Caches, and Blocking
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Performance Experiments with Matrix Multiplication (PDF)
Ideal-Cache Terminology (PDF)
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Problem set 3 (PDF)
Solutions to Problem Set 3 (PDF)
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Lecture 12: Cache-Oblivious Algorithms and Spatial Locality
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Experiments with Cache-Oblivious Matrix Multiplication (PDF)
Experiments with Memory Access and Matrices
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[No problem set]
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Lecture 13: LU Factorization and Partial Pivoting
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[No handout/notebook]
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[No problem set]
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Lecture 14: Cholesky Factorization and other Specialized Solvers. Eigenproblems and Schur Factorizations
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[No handout/notebook]
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[No problem set]
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Lecture 15: Eigensolver Algorithms: Companion Matrices, Ill-Conditioning, and Hessenberg Factorization
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Hessenberg Factorization (PDF)
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[No problem set]
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Lecture 16: The Power Method and the QR Algorithm
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[No handout/notebook]
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[No problem set]
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Lecture 17: Shifted QR and Rayleigh Quotients
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[No handout/notebook]
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[No problem set]
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Lecture 18: Krylov Methods and the Arnoldi Algorithm
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[No handout/notebook]
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[No problem set]
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Lecture 19: Arnoldi and Lanczos with Restarting
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Why Restarting Arnoldi/Lanczos is not Trivial (PDF)
Experiments with Arnoldi Iterations
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[No problem set]
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Lecture 20: The GMRES Algorithm and Convergence of GMRES and Arnoldi
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[No handout/notebook]
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Problem set 4 (PDF)
Solutions to Problem Set 4 (PDF)
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Lecture 21: Preconditioning Techniques. The Conjugate-Gradient Method
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Large-Scale Linear Algebra: Dense Matrix Methods
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[No problem set]
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Lecture 22: Convergence of Conjugate Gradient
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[No handout/notebook]
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[No problem set]
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Lecture 23: Biconjugate Gradient Algorithms
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[No handout/notebook]
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[No problem set]
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Lecture 24: Sparse-Direct Solvers
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Sparse Matrix Algorithms (PDF) (Courtesy of Per-Olof Persson. Used with permission.)
Sparse-Direct Solvers in Julia
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[No problem set]
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Lecture 25: Overview of Optimization Algorithms
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A Brief Overview of Optimization Problems (PDF)
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Midterm exam (PDF)
Solutions to midterm exam (PDF)
Midterm exams and solutions from previous years
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Lecture 26: Adjoint Methods
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Adjoint Methods (PDF)
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[No problem set]
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Lecture 27: Adjoint Methods for Eigenproblems and Recurrence Relations
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Adjoint Methods and Sensitivity Analysis for Recurrence Relations (PDF)
Recurrence Relation
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[No problem set]
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Lecture 28: Trust-Regions Methods and the CCSA Algorithm
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[No handout/notebook]
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[No problem set]
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Lecture 29: Lagrange Dual Problems
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Lagrangian, Lagrange Dual Function and Dual Problem
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[No problem set]
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Lecture 30: Quasi-Newton Methods and the BFGS Algorithm
Lecture 31: Derivation of the BFGS Update
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Quasi-Newton Optimization: Origin of the BFGS Update (PDF)
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[No problem set]
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Lecture 32: Derivative-Free Optimization by Linear and Quadratic Approximations
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[No handout/notebook]
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[No problem set]
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Lecture 33: Numerical Integration and the Convergence of the Trapezoidal Rule
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Numerical Integration and the Redemption of the Trapezoidal Rule (PDF)
Fourier Cosine Series Examples (PDF)
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[No problem set]
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Lecture 34: Clenshaw-Curtis Quadrature
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[No handout/notebook]
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[No problem set]
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Lecture 35: Chebyshev Approximation
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[No handout/notebook]
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[No problem set]
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Lecture 36: Integration with Weight Functions, and Gaussian Quadrature
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[No handout/notebook]
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[No problem set]
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Lecture 37: Adaptive and Multidimensional Quadrature
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[No handout/notebook]
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[No problem set]
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Lecture 38: The Discrete Fourier Transform (DFT) and FFT Algorithms
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Fast Fourier Transform Algorithms (PDF)
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[No problem set]
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Lecture 39: FFT Algorithms and FFTW
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Fast Fourier Transform and Fast Fourier Transform in the West (PDF - 2.6MB)
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[No problem set]
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