Finding Real Roots Using Iteration: How to Choose Starting Values

  • Thread starter bemigh
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In summary, the speaker is seeking assistance in finding the real roots of a given equation using the technique of iteration. They are unsure of which values to start testing and are considering using fixed point iteration by rearranging the function and selecting intervals to test. They are also considering using the midpoint of the interval as their starting value.
  • #1
bemigh
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Hey everyone, I'm not sure where I am going wrong here...
I need to find the 3 roots of the following equation:
x^3 - (6.2)x^2-11x-5=0
and i need to find the real roots using the technique of iteration. I understand this technique, however I am not sure which values i should start off testing...(which x1)
Any help would be appreciated...
Steph
 
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  • #2
this may be misleading but here goes anyway...

do you mena fixed point iteration s.t. you rearrance f(x) to get a convergent sequence? Well pick intervals like [0,1] [1,2] and find the deriavtie at the end points. also find the function at the endpoints
if the the function at one point is negative while hte other is potivie you have a root in that interval and pick maybe the midpoint of the interval since your sequence would converge anyway.
 

1. What is the technique of iteration?

The technique of iteration is a process of repeating a set of instructions or actions in a systematic manner until a desired result is achieved. It is commonly used in various fields of science and technology to solve complex problems or improve efficiency.

2. How does iteration differ from recursion?

Iteration and recursion are both methods of repeating a set of instructions, but they differ in their approach. In iteration, the instructions are repeated using a loop until a specific condition is met, while recursion involves calling a function within itself until a base case is reached.

3. What are some common applications of iteration in science?

Iteration is used in numerous scientific fields, such as mathematics, computer science, and engineering. It is commonly used in numerical analysis to solve complex equations, in computer programming to create loops, and in experimental design to improve and refine methods.

4. What are the benefits of using the technique of iteration?

The technique of iteration allows for the systematic and efficient approach to solving problems. It also allows for the testing and refining of methods, leading to improved efficiency and accuracy. Additionally, it can be easily automated, making it a valuable tool in various scientific and technological processes.

5. Are there any drawbacks to using iteration?

One potential drawback of using iteration is the possibility of getting stuck in an infinite loop if the condition for termination is not properly defined. This can lead to errors and inefficiency in the problem-solving process. Additionally, in some cases, recursion may be a more suitable and efficient approach compared to iteration.

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