Lecture 2 Typeset Notes

Lecture 2 Typeset Notes - ) &amp;amp;lt;0, THEN x R = x App...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. False Position (Regula – Falsi) Method Here obtain [ x L , x R ], such that f(x L ) . f(x R ) <0. Instead of successively bisecting the interval, as in the bisection method, linear interpolation is used to obtain x App such that ( x App , 0) lies on the line joining ( x L , f(x L ) ) and ( x R , f(x R ) ). Since, the points ( x L , f(x L ) ), ( x App , 0) and ( x R , f(x R ) ) all lie on the same line, it is clear that: L R L App L R L x x x x x f x f x f ! ! " ! ! ) ( ) ( ) ( 0 , and hence, ) ( ) ( ) ( R L R L L L App x f x f x x x f x x ! ! ! " . Next we determine which of the 2 sub-intervals [ x L , x App ] or [ x App , x R ] contains the root of f(x) . Algorithm: Given the above, REPEAT ) ( ) ( ) ( R L R L L L App x f x f x x x f x x ! ! ! " IF f(x L ) . f(x App
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) &lt;0, THEN x R = x App ELSE x L = x App UNTIL Stopping criteria are met END Possible stopping criteria # | x L x R | &lt; e for some small e (means we have narrowed down the interval so much that for all intents and purposes we do not need to continue. # n&gt;N limit (means we have exceeded the maximal allowed number of iterations N limit ) # | f(x App ) | &lt; e 2 for some small e 2 (this means that my middle point is almost the root of this function, so no need to continue...
View Full Document

Lecture 2 Typeset Notes - ) &amp;amp;lt;0, THEN x R = x App...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online