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PART 2
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CMPE 30063: NU
REGULA FALSI METHOD/ FALSE
POSITION METHOD
A METHOD WHICH SEEKS UP THE RATE OF CONVERGENCE OF THE
ESTIMATES TO THE ACTUAL ROOT/ LIKE BISECTION METHOD, IT
ASSUMES THAT F IS CONTINUES ON AN INTERVAL AND THAT A
•BETTER APPROXIMATION CAN BE OBTAINED BY TAKING THE STRAIGHT
LINE JOINING THE POINTS AND INTERSECTING THE X-AXIS. TO OBTAIN
THE VALUE OF WE CAN EQUATE THE TWO EXPRESSIONS OF THE
SLOPE M OF THE LINE L.
REGULA FALSI METHOD/ FALSE
POSITION METHOD
ILLUSTRATION:
FORMULA:
�
�
�
� (¿ ¿ � )− �
(¿ ¿ � − � )
¿
� ( ¿ ¿ �) [ �� − � � −� ]
¿
� �+ � = � � − ¿
DERIVATION:
EXAMPLE 1
CONDUCT 4 ITERATIONS: USING REGULA FALSI METHOD.
•
1
2
3
4
SOLUTION
EXAMPLE 2
USE FALSE POSITION METHOD TO SOLVE IN THE EQUATION
•
AT LEAST THREE CORRECT DECIMAL PLACES.
1
2
3
4
5
6
7
SECANT METHOD
THE SECANT METHOD IS SIMILAR TO REGULA-FALSI SCHEME OF
ROOT BRACKETING METHODS BUT DIFFERS IN THE IMPLEMENTATION.
THE REGULA-FALSI METHOD BEGINS WITH THE TWO INITIAL
APPROXIMATIONS AND SUCH THAT WHERE IS THE ROOT OF IT
PROCEEDS TO THE NEXT ITERATION BY CALCULATING USING THE
•ABOVE FORMULA AND THEN CHOOSES ONE OF THE INTERVAL OR
DEPENDING ON OR RESPECTIVELY. ON THE OTHER HAND, SECANT
METHOD STARTS WITH TWO INITIAL APPROXIMATION AND (THEY MAY
NOT BRACKET THE ROOT) AND THEN CALCULATES THE BY THE SAME
FORMULA AS IN REGULA-FALSI METHOD BUT PROCEEDS TO THE NEXT
ITERATION WITHOUT BOTHERING ABOUT ANY ROOT BRACKETING.
SECANT METHOD
ILLUSTRATION:
FORMULA:
�
�
�
� (¿ ¿ � )− �
(¿ ¿ � − � )
¿
� ( ¿ ¿ �) [ �� − � � −� ]
¿
� �+ � = � � − ¿
EXAMPLE 3
SOLVE
USING SECANT METHOD APPROXIMATELY
•
1
2
3
4
5
6
SOLUTION
EXAMPLE 4
USE SECANT METHOD TO SOLVE AT LEAST 5 CORRECT DECIMAL
•PLACES.
1
2
3
4
5
6