Develop a matlab program to find all roots of equation

Assignment Help Mathematics
Reference no: EM131393642

Problem -

Consider the quartic equation

x4 + ax3 + bx2 + cx - 1 = 0,                                             (1)

where a, b, c, and d are real input coefficients. Develop a matlab program to find all roots of equation (1) using the methods discussed in class. Your program can not use the matlab built-in functions fzero, roots, eig, and eigs.

You should turn in a .m file quarticxxx.m which contains a matlab function of the form

function [rts, info] = quarticxxx(C)

where xxx is your student id, C = (a, b, c, d) is the input vector of coefficients, rts is the vector of roots and info is your output message.

Your program will be stress-tested against typical and pathological quartic equations:

1. equations with random C;

2. equations with very large C; or

3. equations with double roots or nearly double roots; or

You will receive partial credit for each correct root (accurate to within a. relative error of at most 10-5, as compared to the roots function in matlab) receive additional credit.

Verified Expert

The solution is implemented in standard matlab language using the algorithm that can be found.This provide a solution for a general quartic of the type ax^4+bx^3+cx^2+dx+e, so in the considered case I applied the method, given a =1 and e = -1, as it was required in the assignment. The other variables are to be given via the C list.The other variables are to be given via the C list. From the screenshot I sent you, you can see that the outcome of the operator roots for matlab is the same (permutated) to the one obtained with the method I implemented. I expect the method to find all the possible roots of the equation, and it should also be quite fast, since it does not involve any matrix operation or such. The only problem may be given by approximation if the values in C are very big, but they are surely below the wanted accuracy of E-5.

Reference no: EM131393642

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Reviews

inf1393642

3/10/2017 4:29:48 AM

Thanks for your complete clarifications, now i'm totally satisfied now. you have done very good job. thanks once again. i have learnt a lot from this tutor.

inf1393642

3/10/2017 4:27:29 AM

https://en.wikipedia.org/wiki/Quartic_function#Solving_a_quartic_equation. A priori the program can be written using the bisection method, as this method converges for every possible function. It just takes time to do that, since the function lives in the complex plane and could have everything from 1 to 4 roots, without counting multiplicity.

inf1393642

3/10/2017 4:27:00 AM

because I spent lots of time to go through the assignment but I found, it didn't use the BISECTION METHOD to develop the function, because BISECTION METHOD should be the method to develop this program. Please let me know how to solve and thank you so much for your time. They explain quite extensively what it is and how it works. The idea behind it is to divide the interval in sub-intervals and find where the function changes sign, there is a zero in that interval, thus you divide it in half, and look for where the function changes sign again, and so on. You have to repeat the procedure for every root you have to find. Can the program written by BISECTION METHOD, because it should be the method that the assignment suggested. I am little worried about it. Let me discuss that with the Grader and see if the assignment can be written by different method. By the way, can you please let me know what method that you used in developing this program? The formula I used is the one accredited to Ludovico Ferrari, you can find it here:

inf1393642

3/10/2017 4:26:32 AM

Thanks for your help. This assignment is quite urgent, So please let me know as soon as possible, Thanks for your understanding. The code is correct. It solves the equation given in the assignment.I don't understand what I tried to do, but I need, since three numbers are needed in order to get a result, but you can get them by calling the function like this: quarticxxx([a b c]) And this will solve x^4 + ax^3 + bx^2 + cx -1 = 0. Again, the code is written to solve this equation and it passed all the tests I did. First of all, Thank you so much for your quick response. I tested the code and it passed it in most of the cases. But there is just one particular case didn't work. I am going to test if the corrected version works and Again thank for you corrections. Did you use Bisection to make the program? I hope you're doing well. As the assignment emphasized, "Develop a MATLAB program to find all roots of equation USING THE METHOD DISCUSS IN CLASS", so even though the function works in all cases but it is NOT what the assignment suggest then it will be penalized.

inf1393642

3/10/2017 4:26:20 AM

The assignment requires developing a math program and it needs to be finished one week from now. I am sure I can complete the assignment IF I am provided the methods they want to implement. That is my only query. I hope you're doing well. It should be great if you're following the instruction that I attached earlier. please let me know if there is anything I need to provide. Thanks for your quick response, it will be great that if the assignment will be completed by the method they (instruction) want to implement. I believe there is an error in the assignment text, but the code works for the required case. It solves the equation x^4+ax^3+bx^2+cx-1=0 using the method you can find here: https://en.wikipedia.org/wiki/Quartic_function#Solving_a_quartic_equation 84112_1TG24WIL220MAT Solution.m Here are the documents that you sent me earlier. 84112_2TG24WIL220MAT Screenshoot Solution.png 84112_3Screen Shot at 125528 PM.png Here is the compressed zip version. 84112_1Math Assignment 1.zip.

len1393642

2/14/2017 12:47:15 AM

The assignment requires developing a math program and it needs to be finished one week from now. Your program will receive 0 points if the strings fzero, roots or eig (all lower case) show up anywhere in your file.

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