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Part1) Implement the interval search method in C. Read a positive integer a from the user of which square root we would like to find. Take the initial interval as (0, a) and divide this interval into 10 equal size sections at each iteration. Repeat this search until the root is found or the difference between x1 and x2 becomes less than 0.0001. Print the resulting value of the root (if one is found) or the value of x1 if the root cannot be found exactly. Hint: You need to check each section to see if the root resides within that section by evaluating f(x) at the section boundaries and looking at the signs of the evaluations. If the section contains the root, then divide the section into 10 new sections and repeat the process

Part1) Implement the interval search method in C. Read a positive integer a from the user of which square root we would like to find. Take the initial interval as (0, a) and divide this interval into 10 equal size sections at each iteration. Repeat this search until the root is found or the difference between x1 and x2 becomes less than 0.0001. Print the resulting value of the root (if one is found) or the value of x1 if the root cannot be found exactly. Hint: You need to check each section to see if the root resides within that section by evaluating f(x) at the section boundaries and looking at the signs of the evaluations. If the section contains the root, then divide the section into 10 new sections and repeat the process

Database System Concepts
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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If the square root of an integer number a is x, then the following equation holds: x 2 = a By moving the constant a to the left side of the equality, we get: f(x) = x 2 - a= 0 Therefore, the roots of the above quadratic function will be the square roots of a. Part1) Implement the interval search method in C. Read a positive integer a from the user of which square root we would like to find. Take the initial interval as (0, a) and divide this interval into 10 equal size sections at each iteration. Repeat this search until the root is found or the difference between x1 and x2 becomes less than 0.0001. Print the resulting value of the root (if one is found) or the value of x1 if the root cannot be found exactly. Hint: You need to check each section to see if the root resides within that section by evaluating f(x) at the section boundaries and looking at the signs of the evaluations. If the section contains the root, then divide the section into 10 new sections and repeat the process. Part2) Implement the Newton-Raphson formula in C. Read a positive integer a from the user of which square root we would like to find. Start with the initial estimate of root as a (i.e., xi = a) and apply the formula in (1) to find the next estimate of the root at each iteration. Repeat the iterations until the difference between the current estimate and the previous estimate of the root becomes less than 0.0001. Print the resulting value of the root (if one is found) or the value of x1 if the root cannot be found exactly.
Transcribed Image Text:If the square root of an integer number a is x, then the following equation holds: x 2 = a By moving the constant a to the left side of the equality, we get: f(x) = x 2 - a= 0 Therefore, the roots of the above quadratic function will be the square roots of a. Part1) Implement the interval search method in C. Read a positive integer a from the user of which square root we would like to find. Take the initial interval as (0, a) and divide this interval into 10 equal size sections at each iteration. Repeat this search until the root is found or the difference between x1 and x2 becomes less than 0.0001. Print the resulting value of the root (if one is found) or the value of x1 if the root cannot be found exactly. Hint: You need to check each section to see if the root resides within that section by evaluating f(x) at the section boundaries and looking at the signs of the evaluations. If the section contains the root, then divide the section into 10 new sections and repeat the process. Part2) Implement the Newton-Raphson formula in C. Read a positive integer a from the user of which square root we would like to find. Start with the initial estimate of root as a (i.e., xi = a) and apply the formula in (1) to find the next estimate of the root at each iteration. Repeat the iterations until the difference between the current estimate and the previous estimate of the root becomes less than 0.0001. Print the resulting value of the root (if one is found) or the value of x1 if the root cannot be found exactly.
If the square root of an integer number a is x, then the following equation holds: x² = a By moving the constant a to the left side of the equality, we get: f(x)=x²-a = 0 Therefore, the roots of the above quadratic function will be the square roots of a. This function's graph is a simple parabola as show below. X1 -a X₂ f(x) root of f(x) If f(x₁) and f(x₂) have opposite signs, then there is at least one root in the interval (x1, x2) as shown above. If the interval is small enough, it is likely to contain a single root. Thus, the roots of f(x) can be detected by repetitively evaluating the function at shrinking intervals (x1, x2) and looking for a change in sign between f(x1) and f(x2).
Transcribed Image Text:If the square root of an integer number a is x, then the following equation holds: x² = a By moving the constant a to the left side of the equality, we get: f(x)=x²-a = 0 Therefore, the roots of the above quadratic function will be the square roots of a. This function's graph is a simple parabola as show below. X1 -a X₂ f(x) root of f(x) If f(x₁) and f(x₂) have opposite signs, then there is at least one root in the interval (x1, x2) as shown above. If the interval is small enough, it is likely to contain a single root. Thus, the roots of f(x) can be detected by repetitively evaluating the function at shrinking intervals (x1, x2) and looking for a change in sign between f(x1) and f(x2).
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