PC20101110

PC20101110 - Numerical Analysis II Dr Abigail Wacher Nov...

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Unformatted text preview: Numerical Analysis II Dr Abigail Wacher Nov 10, 2010 1 Let us use a decimal floating point system F with 4 digits and an exponent between -9 and 9. b = 10, t = 4, u = K L = 9 (Associativity) Take a = 1.000 $ 10 , b = 3.000 $ 10 K 4 , c = 4.000 $ 10 K 4 a C b = 1.000 $ 10 C 0.0003 $ 10 = 1.000 $ 10 a C b C c = 1.000 $ 10 C 0.0004 $ 10 = 1.000 $ 10 b C c = 3.000 $ 10 K 4 C 4.000 $ 10 K 4 = 7.000 $ 10 K 4 a C b C c = 1.000 $ 10 C 0.0007 $ 10 = 1.001 $ 10 Not associative! Uniqueness of solutions to algebraic equations does not hold for floating point arithmetic. 1 C x = 1 has more than 1 solution in F not just the "exact" solution x = 0. In fact in F , every positive floating point number y ! 5.000 $ 10 K 4 is a correct solution to the equation. In the course of solving ax 2 K 2 bx C c = 0, for x , the expression b 2 K ac must be computed. Can the true value of b 2 K ac be non-negative and yet have a negative computed value?...
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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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PC20101110 - Numerical Analysis II Dr Abigail Wacher Nov...

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