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Apr 20, 2024
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MATH 701 - Numerical Analysis and Approximation (3 units)
Norms of vectors and matrices, computation of eigenvalues and eigenvectors, matrix transformations, Weierstrass’ approximation theorem, Chebyshev polynomials, best and uniform approximation, splines, approximation in abstract spaces.
Units of Lecture: 3
Student Learning Outcomes
Upon completion of this course, students will be able to:
1. state and prove basic theorems in numerical linear algebra including Schur’s Theorem, quadratic order of convergence of Newton’s methods and the Gershgorin circle theorem.
2. demonstrate familiarity common algorithms including the shifted QR algorithm of Francis, the algorithms for computation of matrix norms, Gram Schmidt algorithm, Thomas algorithm and Newton’s divided difference formula.
3. recall and define terminology including error, condition number, matrix norm, machine epsilon, unitary matrix, Haar subspace, order of convergence positive definite matrix and stability.
4. write practical computer programs.
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