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Numerical Linear Algebra

Numerical Linear AlgebraWilliam Layton and Myron SussmanUniversity of PittsburghPittsburgh, Pennsylvaniac 2014 William Layton and Myron Sussman. All rights 978-1-312-32985-0 ContentsContentsiIntroductionviiSources 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 .. The Gaussian Elimination Algorithm .. Pivoting Strategies .. Tridiagonal and Banded Matrices .. TheLUdecomposition .. 28iiiCONTENTS2 Norms and Error FENLA and Iterative Improvement .. Vector Norms .. Norms.. Error, Residual and Condition Number.

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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