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Numerical Linear Algebra

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Numerical Linear AlgebraWilliam Layton and Myron SussmanUniversity of PittsburghPittsburgh, Pennsylvaniac 2014 William Layton and Myron Sussman. All rights 978-1-312-32985-0ContentsContentsiIntrod uctionviiSources of Arithmetical Error . . . . . . . . . . . . . . . . xiiMeasuring Errors: The trademarked quantities . . . . . . xixLinear systems and finite precision arithmeticxxiiiVectors and Matrices . . . . . . . . . . . . . . . . . . . . . xxiiiEigenvalues and singular values. . . . . . . . . . . . . . xxviiiError and residual . . . . . . . . . . . . . . . . . . . . . . xxxviWhen is a Linear system solvable? . . . . . . . . . . . . . . xliiWhen is an N N matrix numerically singular? . . . . . . xlviI Direct Methods11 Gaussian Elimination + Backsubstitution . . . . . . . . . . . . Algorithms and pseudocode.

liament], ’Pray, Mr. Babbage, if you put into the ma-chine wrong gures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. - Babbage, Charles (1792-1871) Numerical linear …

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