Transcription of LECTURES IN BASIC COMPUTATIONAL NUMERICAL ANALYSIS
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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 .. Summary of methods for the algebraic eigenvalue problem .. Summary .. 322 Solution of Nonlinear Fixed-Point Methods for Single Nonlinear Equations.
In the case of Euclidean spaces, we can define another useful object related to the Euclidean norm, the inner product (often called the “dot product” when applied to finite-dimensional vectors). Definition 1.3 Let S be a N-dimensional Euclidean space with v,w ∈ S. Then hv,wi ≡ XN i=1 viwi (1.4) is called the inner product.
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