4. The "bi-secant method" is a combination of the secant method and the bisection method. As in the case of the secant method, it uses two points (a, f(a)), (b, f(b)) to find a secant line that goes through those points and computes a point c where the secant intersects the r axis. As in the case of the bisection method, we require that f(a)f(b) < 0, and assuming that a sc
4. The "bi-secant method" is a combination of the secant method and the bisection method. As in the case of the secant method, it uses two points (a, f(a)), (b, f(b)) to find a secant line that goes through those points and computes a point c where the secant intersects the r axis. As in the case of the bisection method, we require that f(a)f(b) < 0, and assuming that a sc
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. The "bi-secant method" is a combination of the secant method and the bisection method.
As in the case of the secant method, it uses two points (a, f(a)), (b, f(b)) to find a secant line
that goes through those points and computes a point c where the secant intersects the r axis.
As in the case of the bisection method, we require that f(a)f(b) < 0, and assuming that
a <c<b the method uses sign change to determine in which side of c the solution is.
(a) Find the equation of the secant line line between the points (a, f(a)) and (b, f(b))
Hint: It helps to visualize this method graphically (draw the points and the line)
(b) Find a point c where the secant line between the points (a, f(a)) and (b, f(b)) intersects
the x-axis
![Question continued
(c) Notice that if there is a sign change in the function from a to c then the solution is in [a, c]
otherwise, the solution is in [c, b]
Use the description above, and your formula for c to write the bi-secant algorithm
such that that given f(r), a, b, e, N returns an approximation to the solution of f(r) with
error tolerance e, or an error, if the number of iterations exceeds N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff26fda3f-4323-495f-b28b-f131dcfa5992%2F62b43f53-4b77-44b4-923f-99e8527f70a1%2Fyg6xmfze_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question continued
(c) Notice that if there is a sign change in the function from a to c then the solution is in [a, c]
otherwise, the solution is in [c, b]
Use the description above, and your formula for c to write the bi-secant algorithm
such that that given f(r), a, b, e, N returns an approximation to the solution of f(r) with
error tolerance e, or an error, if the number of iterations exceeds N
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