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LECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS

J. M. McDonoughUniversity of Kentucky Lexington, KY 40506E-mail: = x [J( )] (x )(m)(m+1)(m)(m) 1D f = 0if fi+1i 12hy = (y,t) LECTURES IN BASIC COMPUTATIONALNUMERICAL ANALYSIS LECTURES IN BASIC COMPUTATIONALNUMERICAL ANALYSISLECTURES IN BASICCOMPUTATIONALNUMERICAL ANALYSISJ. M. McDonoughDepartments of Mechanical Engineering and MathematicsUniversity of Kentuckyc 1984, 1990, 1995, 2001, 2004, 2007 Contents1 NUMERICAL Linear Some BASIC Facts from Linear Algebra .. Solution of Linear Systems .. NUMERICAL solution of linear systems: direct elimination .. NUMERICAL solution of linear systems: iterative methods .. Summary of methods for solving linear systems .. The Algebraic Eigenvalue Problem .. The power method .. Inverse iteration with Rayleigh quotient shifts .. The QR algorithm.

Theorem 1.1 (Cauchy–Schwarz) Let S be an inner-product space with inner product h· ,·i and norm k· k2. If v,w ∈ S, then hv,wi ≤ kvk2 kwk2. (1.5) We have thus far introduced the 2-norm, the infinity norm and the inner product for spaces of finite-dimensional vectors. It is worth mentioning that similar definitions hold as well for ...

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