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, 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 Before beginning our treatment of numerical solution of linear systems we will review a few im-portant facts from linear algebra, itself. We typically think of linear algebra as being associated with vectors and matrices in some finite-dimensional space. But, in fact, most of our ideas extend
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