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Special Topics in Computer Science

by: Allie West II

Special Topics in Computer Science CSCI 2830

Marketplace > University of Colorado at Boulder > ComputerScienence > CSCI 2830 > Special Topics in Computer Science
Allie West II

GPA 3.51

Clayton Lewis

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Clayton Lewis
Class Notes
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This 2 page Class Notes was uploaded by Allie West II on Thursday October 29, 2015. The Class Notes belongs to CSCI 2830 at University of Colorado at Boulder taught by Clayton Lewis in Fall. Since its upload, it has received 25 views. For similar materials see /class/231987/csci-2830-university-of-colorado-at-boulder in ComputerScienence at University of Colorado at Boulder.

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Date Created: 10/29/15
December 8 2008 CSCI 2830 Final Hour Exam Review Final Hour Exam Saturday December 13 730 10am in ECCR 116 This exam will cover all material speci ed on the web site for October 7 through December 9 not including the guest presentations Bring lots of pencils and erasersi Paper will be provided No other supplies books notes calculators etc will be allowed 1 Stability a Fundamental Axiom of FloatingPoint Arithmetic p99 b relative error vs absolute error c forward stability de nition and how to de termine d backward stability de nition e machine epsilon 06M f what does instability mean for the quality of the solution E0 Backward error analysis a how to perform a simple backward error ysis b backward stability of QR factorization c backward stability of backsubstitution CA3 i Conditioning and stability of least squares prob ems a what is conditioning how is it different from stability b matrix condition number c what does illconditioning mean for the quality of the solution d stability of Householder triangularization e instability of GramSchmidt and how to im prove f stability vs conditioning of normal equa tions g i Gaussian elimination and pivoting a elementary matrix 5 533 7 b GE without pivoting in terms of elementary matrices c solving AI 12 via LU d instability of GE without pivoting e how to pivot f GE with pivoting in terms of elementary matrices and permutations g partial and complete pivoting which is used in practice Stability of Gaussian elimination a stability of LU b growth factors c worst case instabilit y d stability of partial pivoting in practice Cholesky factorization a symmetric positive de nite matrices b why Cholesky is cheaper than LU c stability Eigenvalue problems and algorithms a characteristic polynomial b geometric and algebraic multiplicities c normal matrix d similarity transformations e defective matrices f diagonalizability g how determinant and trace relate to eigen values h Schur factorization i the three eigenvaluerevealing factoriza tions p188 two phases of eigenvalue computation Reduction to Hessenberg or tridiagonal form a what is Hessenberg form b when is a Hessenberg matrix tridiagonal Householder reduction to Hessenberg form c d cost of tridiagonal vs Hessenberg reduc tions e stability of Hessenberg reduction H H E0 H 9 Rayleigh quotient inverse iteration what is the Rayleigh qutotient of a matrix power methodwhatls good and bad about it how inverse iteration derives from the 15 power method how do the power method and inverse iter ation wor i costs of methods for tridiagonal vs dense matrices The QR algorithm the pure QR algorithm the practical QR algorithm Wilkinson shift de ned not formula stability and accuracy of QR Algorithms for eigenvalue problems and the SVD a bisection and inverse iteration b basic idea of divide and conquer c relationship of SVD and eigendecomposi tion d GolubKahan bidiagonaization e two phases of SVD computation lterative methods a why iterate b sparsity c Krylov subspace d exact vs approximate solution The Arnoldi iteration a What does this algorithm compute b On what kind of matrices does the algo rithm operate c Given a copy of the algorithm what does each step or group of steps do d Why does it make sense that those steps lead to the result GMRES a What does this algorithm compute b On what kind of matrices does the algo rithm operate c Given a copy of the algorithm what does each step or group of steps or d Why does it make sense that those steps lead to the result i Lanczos method and conjugate gradient a conjugate directions b What do these algorithms compute c On what kind of matrices do the algorithms operate d Given a copy of the algorithm what does each step or group of steps do e Why does it make sense that those steps lead to the resu ti


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