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Introduction to Numerical Methods >> Content Detail



Study Materials



Readings

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This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.

The required textbook for this class is:

Amazon logo Trefethen and Bau. Numerical Linear Algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1997, ISBN: 0898713617. (Abbreviated "NLA")

Other readings include:

Amazon logo Bai, et al. Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000. ISBN: 0898714710. (Abbreviated "Eig")

Amazon logo Barrett, et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1993. ISBN: 0898713285. (Abbreviated "It")

Shewchuk, Jonathan R. "An Introduction to the Conjugate Gradient Method Without the Agonizing Pain." Carnegie Mellon University (August 1994). (Abbreviated "CG") (PDF)#

Goldberg, David. What Every Computer Scientist Should Know About Floating Point Arithmetic. ACM Computing Surveys 23, no. 1 (March 1991): 5-48. (Abbreviated "FP")


LEC #TOPICSREADINGS
1Introduction, Basic Linear AlgebraNLA 1
2Orthogonal Vectors and Matrices, NormsNLA 2 and 3
3The Singular Value DecompositionNLA 4 and 5
4The QR FactorizationNLA 6 and 7
5Gram-Schmidt OrthogonalizationNLA 8
6Householder Reflectors and Givens RotationsNLA 10
7Least Squares ProblemsNLA 11
8Floating Point Arithmetic, The IEEE StandardNLA 13, FP
9Conditioning and Stability INLA 12, 14, and 15
10Conditioning and Stability IINLA 16 and 17
11Gaussian Elimination, The LU FactorizationNLA 20 and 21
12Stability of LU, Cholesky FactorizationNLA 22 and 23
13Eigenvalue ProblemsNLA 24 and 25
14Hessenberg / Tridiagonal ReductionNLA 26
15The QR Algorithm INLA 27 and 28
16The QR Algorithm IINLA 29
17Other Eigenvalue AlgorithmsNLA 30
18The Classical Iterative MethodsIt 2.2
19The Conjugate Gradients Algorithm INLA 38, CG
20The Conjugate Gradients Algorithm IINLA 38, CG
21Sparse Matrix AlgorithmsIt 4.3, Eig
22Preconditioning, Incomplete FactorizationsNLA 40, It 3
23Arnoldi / Lanczos IterationsNLA 33 and 36
24GMRES, Other Krylov Subspace MethodsNLA 35 and 39, It 2.3
25Linear Algebra SoftwareEig

 








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