tut1 - cep 2008/09 MT3802 - Numerical Analysis Tutorial...

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Unformatted text preview: cep 2008/09 MT3802 - Numerical Analysis Tutorial Sheet 1 1. Show that the following satisfy the requirements of a norm specified on a Vector Space: (i) b f = a |f (x)|dx where f (x) C[a, b] ; (ii) x = max |xi | 1in where x Rn . 2. An inner product is defined as a function that associates a real number x, y with each pair of vectors x and y in a Vector Space such that x, y = y, x x + y, z = x, z + y, z x, y = x, y x, x > 0 all x = 0 Since x + y, x + y 0 for all x, y and , use the above axioms to deduce the Cauchy-Schwarz inequality x, y For f, g C[a, b] and f , g defined as b 2 x, x y, y . f, g = a f (x)g(x)dx show that 1/2 b (f (x))2 dx a is a norm on C[a, b]. 3. By considering the quantity ( x p )p , p 1, show that x p x p x p n and deduce lim x p . ...
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This note was uploaded on 09/28/2009 for the course MATH MATH427 taught by Professor Dr.sharpey during the Spring '09 term at Monmouth IL.

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