Lecture20110120_1

Lecture20110120_1 - Djoko Wirosoetisno CM322 (Thurs...

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Homeworks by Friday Noon CM322 Outline Term 1. 1) Root-finding 2) Polynomial Interpolation 3) Numerical Differentiation Term 2. 4) Linear Algebra 5) l 2 approximations 6) Numerical Integration Linear Systems Problem: Solve, over = or , the system: a 11 x 1 C 12 2 C ... C 1 n = b 1 ... n1 1 C ... C nn = 5 Ax = Issues i) Efficiency: minimise work for large . (think ~ 10 6 ) ii) Accuracy: Minimise round-off errors when using floating-point arithmetic. Linear Algebra Review A is an # matrix. Definition Transpose u : u ij = ji symmetric: u = skew symmetric u = K Definition non singular c d that solves = Facts non-singular 0 d ! that solves = non-singular 5 d ! K 1 st c , = K 1 non-singular 5 detA 0 Definition positive definite $ O 0 c positive semidefinite 5 $ 0 c Fact positive definite 0 non-singular Gaussian Elimination Try to solve = given , Start with of special forms. Definition
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This note was uploaded on 02/09/2011 for the course MATH 2051 taught by Professor Dr.a.wacher during the Fall '11 term at Durham.

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Lecture20110120_1 - Djoko Wirosoetisno CM322 (Thurs...

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