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# sheet - ASE 311 Engineering computation Fall 2009 Review...

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ASE 311 Engineering computation, Fall 2009 Review sheet for the second mid-term exam 3 Matrix computations Chapra: Chapters 10–12, Appendix A 3.2 LU factorization How many operations are needed (approximately) for a) the LU factorization of a u1D45B × u1D45B -matrix [ u1D434 ]? b) the solution of [ u1D434 ][ u1D465 ] = [ u1D44F ] when the triangular factorization of [ u1D434 ] is known? What is the the LU factorization of an u1D45B by u1D45B matrix [ u1D434 ], and how is it related to Gauss elimination? Does it always exist? What is the Cholesky factorization and for what kind of matrices is it applicable? 3.3 Matrix inverse and condition How can the LU factorization be utilized in the computation of the matrix inverse? How is the condition number u1D705 ( u1D434 ) of a matrix [ u1D434 ] defined? How does u1D705 ( u1D434 ) relate to perturbations in the solution [ u1D465 ] to a linear system [ u1D434 ][ u1D465 ] = [ u1D44F ], when [ u1D434 ] and [ u1D44F ] are perturbed? 3.4 Iterative methods For what type of linear systems are iterative methods to be preferred to Gauss elimination?

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