CSC_349_HANDOUT#11

# CSC_349_HANDOUT#11 - 1 COMPUTER SCIENCE 349A Handout Number...

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Unformatted text preview: 1 COMPUTER SCIENCE 349A Handout Number 11 ORDER OF CONVERGENCE OF THE SECANT METHOD AND BISECTION METHOD The Secant method iterative formula is ) ( ) ( ) ( 1 1 1 − − + − − − = i i i i i i i x f x f x x x f x x . Therefore, if t x denotes an exact zero of ) ( x f , ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − − − ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − − − = − − − − = − − − − − − − − − + t i t i t i i i i i i i i i t i t i i i i i i t i t i x x x x x f x f x x x f x f x x x f x f x x x x x f x f x x x f x x x x 1 1 1 1 1 1 1 1 1 ) ( ) ( ) ( ) ( ) ( ) ( 1 ) )( ( ) ( ) ( ) ( ) ( By the Mean Value Theorem, the first large square bracket term above is equal to ) ( 1 i f ξ ′ , for some value 1 and between − i i i x x ξ . The term in the second large square bracket above is equal to 2 ) ( i f η ′ ′ , for some value i η in an interval spanned by t i i x x x and , 1 − as this is a “second divided difference”...
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## This note was uploaded on 12/10/2011 for the course CSC 349 taught by Professor Oadje during the Spring '11 term at University of Victoria.

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CSC_349_HANDOUT#11 - 1 COMPUTER SCIENCE 349A Handout Number...

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