Inverse Quadratic Interpolation and the secant method
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I am currently completing a maths project that aims to approximate the roots of functions using MATLAB.
The two root finding methods that I have used are inverse quadratic interpolation and the secant method.
I have written scripts for both methods and have obtained approximations to the roots of different functions.
I was wondering if it was possible to graphically illustrate the various iterations for a specific function, on the same graph, to show the method converging to the actual root value?
If this is possible I would like to be able to complete it on MATLAB if not then excel?
Does anyone know if this is possible or even how to go about completing it?
Thank you!!
roots matlab
asked Apr 5 '14 at 13:54
projectone
34
add a comment |
up vote
0
down vote
favorite
I am currently completing a maths project that aims to approximate the roots of functions using MATLAB.
The two root finding methods that I have used are inverse quadratic interpolation and the secant method.
I have written scripts for both methods and have obtained approximations to the roots of different functions.
I was wondering if it was possible to graphically illustrate the various iterations for a specific function, on the same graph, to show the method converging to the actual root value?
If this is possible I would like to be able to complete it on MATLAB if not then excel?
Does anyone know if this is possible or even how to go about completing it?
Thank you!!
roots matlab
asked Apr 5 '14 at 13:54
projectone
34
I can't tell you how, but it is doable, no doubt. I would just like to stress that you won't be able to show many iterations as such, because the drawing accuracy will quickly be reached. It is advisable to plot the logarithm of the (absolute) difference to the exact root (which you will precompute), to magnify the scale.
– Yves Daoust
Jun 6 '16 at 19:10
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am currently completing a maths project that aims to approximate the roots of functions using MATLAB.
The two root finding methods that I have used are inverse quadratic interpolation and the secant method.
I have written scripts for both methods and have obtained approximations to the roots of different functions.
I was wondering if it was possible to graphically illustrate the various iterations for a specific function, on the same graph, to show the method converging to the actual root value?
If this is possible I would like to be able to complete it on MATLAB if not then excel?
Does anyone know if this is possible or even how to go about completing it?
Thank you!!
roots matlab
asked Apr 5 '14 at 13:54
projectone
34
I am currently completing a maths project that aims to approximate the roots of functions using MATLAB.
The two root finding methods that I have used are inverse quadratic interpolation and the secant method.
I have written scripts for both methods and have obtained approximations to the roots of different functions.
I was wondering if it was possible to graphically illustrate the various iterations for a specific function, on the same graph, to show the method converging to the actual root value?
If this is possible I would like to be able to complete it on MATLAB if not then excel?
Does anyone know if this is possible or even how to go about completing it?
Thank you!!
roots matlab
roots matlab
asked Apr 5 '14 at 13:54
projectone
34
asked Apr 5 '14 at 13:54
projectone
34
asked Apr 5 '14 at 13:54
projectone
34
asked Apr 5 '14 at 13:54
projectone
34
asked Apr 5 '14 at 13:54
projectone
34
34
I can't tell you how, but it is doable, no doubt. I would just like to stress that you won't be able to show many iterations as such, because the drawing accuracy will quickly be reached. It is advisable to plot the logarithm of the (absolute) difference to the exact root (which you will precompute), to magnify the scale.
– Yves Daoust
Jun 6 '16 at 19:10
add a comment |
I can't tell you how, but it is doable, no doubt. I would just like to stress that you won't be able to show many iterations as such, because the drawing accuracy will quickly be reached. It is advisable to plot the logarithm of the (absolute) difference to the exact root (which you will precompute), to magnify the scale.
– Yves Daoust
Jun 6 '16 at 19:10
I can't tell you how, but it is doable, no doubt. I would just like to stress that you won't be able to show many iterations as such, because the drawing accuracy will quickly be reached. It is advisable to plot the logarithm of the (absolute) difference to the exact root (which you will precompute), to magnify the scale.
– Yves Daoust
Jun 6 '16 at 19:10
I can't tell you how, but it is doable, no doubt. I would just like to stress that you won't be able to show many iterations as such, because the drawing accuracy will quickly be reached. It is advisable to plot the logarithm of the (absolute) difference to the exact root (which you will precompute), to magnify the scale.
– Yves Daoust
Jun 6 '16 at 19:10
add a comment |
1 Answer
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This is just a suggestion. Create a table $[n_1,x_{n_1}]$ where $n_1$ is the iteration number and $x_n$ the predicted value for the solution using method $1$. Do the same for method $2$ creating a table $[n_2,x_{n_2}]$. Now, plot the values of $x_{n_1}$ and $x_{n_2}$ as a function of $n$. Eventually, add to the plot the horizontal line corresponding to the exact solution.
Is this totally stupid or undoable (I don't know Matlab) ?
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
Hey! Thanks for your suggestion! I don't think I explained myself particularly well so apologies!! Basically, I have created scripts using MATLAB that will compute + then output an approximation for the root of a function using the secant method and inverse quadratic interpolation (IQI) method. These methods use initial root approximations and then keep repeating the process, using the new approximation and the latter one (secant) or two (IQI) until convergence occurrs. I was wondering if there was anyway to display all the iterations on the one graph just to illustrate convergence.
– projectone
Apr 5 '14 at 15:03
For the secant method for example; I would like to have a graph of the function I am investigating and then on this graph I was wondering if it was possible to show all the different lines that MATLAB used to compute the root?
– projectone
Apr 5 '14 at 15:09
! commons.wikimedia.org/wiki/File:Secant_method_2.svg I was hoping that I could achieve something like this image where the blue lines represent the different iterations? Thank you very much for replying though! :)
– projectone
Apr 5 '14 at 15:11
add a comment |
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up vote
0
down vote
This is just a suggestion. Create a table $[n_1,x_{n_1}]$ where $n_1$ is the iteration number and $x_n$ the predicted value for the solution using method $1$. Do the same for method $2$ creating a table $[n_2,x_{n_2}]$. Now, plot the values of $x_{n_1}$ and $x_{n_2}$ as a function of $n$. Eventually, add to the plot the horizontal line corresponding to the exact solution.
Is this totally stupid or undoable (I don't know Matlab) ?
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
Hey! Thanks for your suggestion! I don't think I explained myself particularly well so apologies!! Basically, I have created scripts using MATLAB that will compute + then output an approximation for the root of a function using the secant method and inverse quadratic interpolation (IQI) method. These methods use initial root approximations and then keep repeating the process, using the new approximation and the latter one (secant) or two (IQI) until convergence occurrs. I was wondering if there was anyway to display all the iterations on the one graph just to illustrate convergence.
– projectone
Apr 5 '14 at 15:03
For the secant method for example; I would like to have a graph of the function I am investigating and then on this graph I was wondering if it was possible to show all the different lines that MATLAB used to compute the root?
– projectone
Apr 5 '14 at 15:09
! commons.wikimedia.org/wiki/File:Secant_method_2.svg I was hoping that I could achieve something like this image where the blue lines represent the different iterations? Thank you very much for replying though! :)
– projectone
Apr 5 '14 at 15:11
add a comment |
up vote
0
down vote
This is just a suggestion. Create a table $[n_1,x_{n_1}]$ where $n_1$ is the iteration number and $x_n$ the predicted value for the solution using method $1$. Do the same for method $2$ creating a table $[n_2,x_{n_2}]$. Now, plot the values of $x_{n_1}$ and $x_{n_2}$ as a function of $n$. Eventually, add to the plot the horizontal line corresponding to the exact solution.
Is this totally stupid or undoable (I don't know Matlab) ?
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
Hey! Thanks for your suggestion! I don't think I explained myself particularly well so apologies!! Basically, I have created scripts using MATLAB that will compute + then output an approximation for the root of a function using the secant method and inverse quadratic interpolation (IQI) method. These methods use initial root approximations and then keep repeating the process, using the new approximation and the latter one (secant) or two (IQI) until convergence occurrs. I was wondering if there was anyway to display all the iterations on the one graph just to illustrate convergence.
– projectone
Apr 5 '14 at 15:03
For the secant method for example; I would like to have a graph of the function I am investigating and then on this graph I was wondering if it was possible to show all the different lines that MATLAB used to compute the root?
– projectone
Apr 5 '14 at 15:09
! commons.wikimedia.org/wiki/File:Secant_method_2.svg I was hoping that I could achieve something like this image where the blue lines represent the different iterations? Thank you very much for replying though! :)
– projectone
Apr 5 '14 at 15:11
add a comment |
up vote
0
down vote
up vote
0
down vote
This is just a suggestion. Create a table $[n_1,x_{n_1}]$ where $n_1$ is the iteration number and $x_n$ the predicted value for the solution using method $1$. Do the same for method $2$ creating a table $[n_2,x_{n_2}]$. Now, plot the values of $x_{n_1}$ and $x_{n_2}$ as a function of $n$. Eventually, add to the plot the horizontal line corresponding to the exact solution.
Is this totally stupid or undoable (I don't know Matlab) ?
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
This is just a suggestion. Create a table $[n_1,x_{n_1}]$ where $n_1$ is the iteration number and $x_n$ the predicted value for the solution using method $1$. Do the same for method $2$ creating a table $[n_2,x_{n_2}]$. Now, plot the values of $x_{n_1}$ and $x_{n_2}$ as a function of $n$. Eventually, add to the plot the horizontal line corresponding to the exact solution.
Is this totally stupid or undoable (I don't know Matlab) ?
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
answered Apr 5 '14 at 14:14
Claude Leibovici
117k1156131
117k1156131
Hey! Thanks for your suggestion! I don't think I explained myself particularly well so apologies!! Basically, I have created scripts using MATLAB that will compute + then output an approximation for the root of a function using the secant method and inverse quadratic interpolation (IQI) method. These methods use initial root approximations and then keep repeating the process, using the new approximation and the latter one (secant) or two (IQI) until convergence occurrs. I was wondering if there was anyway to display all the iterations on the one graph just to illustrate convergence.
– projectone
Apr 5 '14 at 15:03
For the secant method for example; I would like to have a graph of the function I am investigating and then on this graph I was wondering if it was possible to show all the different lines that MATLAB used to compute the root?
– projectone
Apr 5 '14 at 15:09
! commons.wikimedia.org/wiki/File:Secant_method_2.svg I was hoping that I could achieve something like this image where the blue lines represent the different iterations? Thank you very much for replying though! :)
– projectone
Apr 5 '14 at 15:11
add a comment |
Hey! Thanks for your suggestion! I don't think I explained myself particularly well so apologies!! Basically, I have created scripts using MATLAB that will compute + then output an approximation for the root of a function using the secant method and inverse quadratic interpolation (IQI) method. These methods use initial root approximations and then keep repeating the process, using the new approximation and the latter one (secant) or two (IQI) until convergence occurrs. I was wondering if there was anyway to display all the iterations on the one graph just to illustrate convergence.
– projectone
Apr 5 '14 at 15:03
For the secant method for example; I would like to have a graph of the function I am investigating and then on this graph I was wondering if it was possible to show all the different lines that MATLAB used to compute the root?
– projectone
Apr 5 '14 at 15:09
! commons.wikimedia.org/wiki/File:Secant_method_2.svg I was hoping that I could achieve something like this image where the blue lines represent the different iterations? Thank you very much for replying though! :)
– projectone
Apr 5 '14 at 15:11
Hey! Thanks for your suggestion! I don't think I explained myself particularly well so apologies!! Basically, I have created scripts using MATLAB that will compute + then output an approximation for the root of a function using the secant method and inverse quadratic interpolation (IQI) method. These methods use initial root approximations and then keep repeating the process, using the new approximation and the latter one (secant) or two (IQI) until convergence occurrs. I was wondering if there was anyway to display all the iterations on the one graph just to illustrate convergence.
– projectone
Apr 5 '14 at 15:03
Hey! Thanks for your suggestion! I don't think I explained myself particularly well so apologies!! Basically, I have created scripts using MATLAB that will compute + then output an approximation for the root of a function using the secant method and inverse quadratic interpolation (IQI) method. These methods use initial root approximations and then keep repeating the process, using the new approximation and the latter one (secant) or two (IQI) until convergence occurrs. I was wondering if there was anyway to display all the iterations on the one graph just to illustrate convergence.
– projectone
Apr 5 '14 at 15:03
For the secant method for example; I would like to have a graph of the function I am investigating and then on this graph I was wondering if it was possible to show all the different lines that MATLAB used to compute the root?
– projectone
Apr 5 '14 at 15:09
For the secant method for example; I would like to have a graph of the function I am investigating and then on this graph I was wondering if it was possible to show all the different lines that MATLAB used to compute the root?
– projectone
Apr 5 '14 at 15:09
! commons.wikimedia.org/wiki/File:Secant_method_2.svg I was hoping that I could achieve something like this image where the blue lines represent the different iterations? Thank you very much for replying though! :)
– projectone
Apr 5 '14 at 15:11
! commons.wikimedia.org/wiki/File:Secant_method_2.svg I was hoping that I could achieve something like this image where the blue lines represent the different iterations? Thank you very much for replying though! :)
– projectone
Apr 5 '14 at 15:11
add a comment |
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I can't tell you how, but it is doable, no doubt. I would just like to stress that you won't be able to show many iterations as such, because the drawing accuracy will quickly be reached. It is advisable to plot the logarithm of the (absolute) difference to the exact root (which you will precompute), to magnify the scale.
– Yves Daoust
Jun 6 '16 at 19:10