Write a code (phyton) implementing the Trisection method, which is analogous to the Bisection method except that at each step, the interval is subdivided into 3 equal subintervals, instead of 2; then takes a subinterval where the function values at the endpoints are of opposite signs. (i) Is the Trisection method guaranteed to converge if for the initial interval [a, b], we have f(a)f(b) < 0? Why or why not? (ii) Starting with several different initial intervals, solve e^x = x^2 using the Trisection method to within 6 correct decimal places. Compare with the results obtained using the Bisection Method.
Write a code (phyton) implementing the Trisection method, which is analogous to the Bisection method except that at each step, the interval is subdivided into 3 equal subintervals, instead of 2; then takes a subinterval where the function values at the endpoints are of opposite signs. (i) Is the Trisection method guaranteed to converge if for the initial interval [a, b], we have f(a)f(b) < 0? Why or why not? (ii) Starting with several different initial intervals, solve e^x = x^2 using the Trisection method to within 6 correct decimal places. Compare with the results obtained using the Bisection Method.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Write a code (phyton) implementing the Trisection method, which is analogous to the Bisection method except that at each step, the interval is subdivided into 3 equal subintervals, instead of 2; then takes a subinterval where the function values at the endpoints are of opposite signs.
(i) Is the Trisection method guaranteed to converge if for the initial interval [a, b], we have f(a)f(b) < 0? Why or why not?
(ii) Starting with several different initial intervals, solve e^x = x^2 using the Trisection method to within 6 correct decimal places. Compare with the results obtained using the Bisection Method.
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