How to Find Roots of Equations Using Iteration Methods and Regula Falsi?

In summary, the conversation is discussing two questions asking for help in solving equations using iteration and the method of Regula Falsi. The first question asks to find the root of a specific equation with six decimal place accuracy and the second question asks to solve an equation using only six iterations and accuracy to four decimal places. The person responding asks for clarification on the iteration method and which root is being referred to in the first question, and also asks for more information on the method of Regula Falsi in the second question. They also remind the original poster to show their efforts in order to receive help.
  • #1
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  • #2
This thread belongs to the homework section (do not repost though, the moderators will move it).

In order to get help, you need to show some efforts.
 
  • #3
I've moved this to the homework section.

First question: Find the root of the equation [itex]x^3- 3x+ 1= 0[/itex] by iteration method (six decimal place accuracy).

There are a number of "iteration methods". Are you referring to a particular one? Why don't you select some starting value and show us how you would start the iteration? Also, this equation has 3 real roots. Which one do you mean by "the" root?

Second question: Use the method of Regula Falsi (method of false position) to solve the equation [itex]j(x)= e^x- 3x[/itex]. (Only six iterations are required, accuracy to 4 decimal places.)

First, was this exactly what the problem says? I don't see an equation, just a function- unless "j(x)" has some meaning you didn't mention.

What is "Regula Falsi"?
 
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1. What is Numerical Analysis 2?

Numerical Analysis 2 is a branch of mathematics that focuses on using numerical methods to solve mathematical problems. It involves using algorithms and computer programs to approximate and solve mathematical equations.

2. What are some common applications of Numerical Analysis 2?

Numerical Analysis 2 has many applications in different fields, such as engineering, physics, economics, and computer science. Some common applications include solving differential equations, finding roots of equations, and optimizing functions.

3. What are some commonly used numerical methods in Numerical Analysis 2?

Some commonly used numerical methods in Numerical Analysis 2 include Newton's method, Euler's method, Gaussian elimination, and Runge-Kutta methods. These methods are used to approximate solutions to mathematical problems.

4. What are the benefits of using numerical methods in Numerical Analysis 2?

Using numerical methods in Numerical Analysis 2 allows us to solve complex mathematical problems that may not have analytical solutions. It also helps us to obtain more accurate results compared to manual calculations and saves time and effort.

5. How is Numerical Analysis 2 different from Numerical Analysis 1?

Numerical Analysis 2 builds upon the concepts and methods learned in Numerical Analysis 1 and applies them to more advanced mathematical problems. It often involves solving systems of equations, higher order differential equations, and more complex functions.

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