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LECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS

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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, 2007Contents1 NUMERICAL Linear Some BASIC Facts from Linear Algebra . . . . . . . . . . . . . . . . .. . . . . . . . . Solution of Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . NUMERICAL solution of linear systems: direct elimination.

1.1. SOME BASIC FACTS FROM LINEAR ALGEBRA 3 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.

  Analysis, Basics, Numerical, Numerical analysis

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