571_syllabus - Math 571 – Syllabus Week 1: Sept. 7: Sept....

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Unformatted text preview: Math 571 – Syllabus Week 1: Sept. 7: Sept. 9: Week 2: Sept. 14: Sept. 16: Week 3: Sept. 21: Sept. 23: Week 4: Sept. 28: Sept. 30: Week 5: Oct. 5: Oct. 7: Week 6: Oct. 12: Oct. 14: Week 7: Oct. 19: Oct. 21: Week 8: Oct. 26: Oct. 28: Week 9: Nov. 2: Nov. 4: Introduction and Lectures 1, 2, and 3: Matrix‐vector multiplication, orthogonal vectors and matrices, norms. Lectures 4 and 5: The singular value decomposition. Lectures 6 and 7: Projectors, QR factorization. Lectures 8 and 10: Gram‐Schmidt orthogonalization, Householder triangularization. Lecture 11: Least squares problems. Lecture 12: Conditioning and condition numbers. Lecture 13: Floating point arithmetic. Lectures 14 and 15: Stability. Lecture 16: Stability of Householder triangularization. Lecture 17: Stability of back substitution. Lecture 18: Conditioning of least squares problems. Lecture 19: Stability of least squares algorithm.s Fall study break. In class MIDTERM. Lectures 20 and 21: Gaussian elimination, pivoting. Lectures 22 and 23: Stability of Gaussian elimination, Cholesky factorization. Lectures 24 and 25: Eigenvalue problems, review of eigenvalue algorithms. Lectures 26 and 27: Reduction to Hessenberg or tridiagonal form, Rayleigh quotient, inverse iteration. Week 10: Nov. 9: Nov. 11: Week 11: Nov. 16: Nov. 18: Week 12: Nov. 23: Nov. 25: Week 13: Nov. 30: Dec. 2: Week 14: Dec. 7: Dec. 9: Lectures 28 and 29: QR algorithm, without and with shifts. Lecture 30: Other eigenvalue algorithms. Lecture 31: Computing the SVD. Lectures 32 and 33: Overview of iterative methods, Arnoldi iteration. Lecture 35: GMRES. Thanksgiving. Lecture 36: Lanczos iteration. Lecture 37: Lanczos iteration and Gauss quadrature. Lecture 38: Conjugate gradients. Lecture 40: Preconditioning. ...
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This note was uploaded on 01/14/2011 for the course MATH 571 taught by Professor Staff during the Winter '08 term at University of Michigan.

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