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by: Addison Beer


Addison Beer
GPA 3.76


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Class Notes
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This 1 page Class Notes was uploaded by Addison Beer on Wednesday September 9, 2015. The Class Notes belongs to MATH 584 at University of Washington taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/192093/math-584-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15
AMATHMATH 584 FINAL REVIEW FALL 2007 This is not an exhaustive list but a summary of what you should review or study The nal will based on material in Trefethen Lectures 1717 20 28 focusing on material covered in lecture and homework Additionally the summary ODE lecture notes posted on the website You may use 3 full sheets 6 fronts and backs of notes NO COMPUTERS OR CALCULATORS USE OF MATLAB F Summary of Topics 1 Pre Midterm Material see MidtermTopicSummarypdf posted on website 2 Gaussian Elimination Relation to LU factorization Partial Pivoting and relation to LU factorization Solving the square system Am b using LU factorization with pivoting ie forward and back substitution Cholesky factorization when is it used 3 Eigenvalues Meaning of eigenvalues eigenvectors algebraic multiplicity and geometric multiplicity Meaning of normal and defective matrices Connection between normal matrices defective matrices and eigenvalue decompositions of ma trices Meaning of the Schur factorization Power lnverse Power with shifts Rayleigh quotient iteration for real symmetric matrices Reduction to Hessenberg form Basic idea of QR algorithm Algorithm 281 and 283 and Theorem 283not the proof just the basic idea 4 ODEs Lecture notes posted on the website is what you should consult Here is a summary Problem stability Basic Linear Multistep Methods Forward and Backward Euler Trapezoid and Midpoint Explicit vs lmplicit schemes Root solving using Newton iteration and connection to implicit schemes Global error Truncation error and consistency Convergence de nition and idea Numerical stability Absolute stability What do absolute stability regions imply about the numerical solution Connection between problem eigenvalues absolute stability and choice of numerical method


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