Gaussian Elimination without pivot












1












$begingroup$


click here for question



I understand Gaussian elim and the inverse, but am new to Gaussian elim without pivot. Wordiness of the question is also throwing me off. Any help will be much appreciated, thanks in advance!






calculus matrices numerical-methods gaussian-elimination







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$endgroup$












  • $begingroup$
    You need to find $(I-A)^{-1}$?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 13:52










  • $begingroup$
    Yeah not sure how to do it without pivot
    $endgroup$
    – RBadger
    Mar 8 '18 at 14:20










  • $begingroup$
    First of all, you need to find $B=I-A$. Then, anything you do for finally calculating by GE should also be applied to $I$, then after all steps, you applied to $I$ you will find a matrix that is $(I-A)_{-1}$. Can you take it from here?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:52










  • $begingroup$
    If you need a comprehensive answer, include matrix $A$ in your question here.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:02










  • $begingroup$
    I don’t understand how to get matrix A, I think after I get the matrix I should be okay
    $endgroup$
    – RBadger
    Mar 9 '18 at 13:02
















1












$begingroup$


click here for question



I understand Gaussian elim and the inverse, but am new to Gaussian elim without pivot. Wordiness of the question is also throwing me off. Any help will be much appreciated, thanks in advance!






calculus matrices numerical-methods gaussian-elimination







share|cite|improve this question









$endgroup$












  • $begingroup$
    You need to find $(I-A)^{-1}$?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 13:52










  • $begingroup$
    Yeah not sure how to do it without pivot
    $endgroup$
    – RBadger
    Mar 8 '18 at 14:20










  • $begingroup$
    First of all, you need to find $B=I-A$. Then, anything you do for finally calculating by GE should also be applied to $I$, then after all steps, you applied to $I$ you will find a matrix that is $(I-A)_{-1}$. Can you take it from here?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:52










  • $begingroup$
    If you need a comprehensive answer, include matrix $A$ in your question here.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:02










  • $begingroup$
    I don’t understand how to get matrix A, I think after I get the matrix I should be okay
    $endgroup$
    – RBadger
    Mar 9 '18 at 13:02














1












1








1





$begingroup$


click here for question



I understand Gaussian elim and the inverse, but am new to Gaussian elim without pivot. Wordiness of the question is also throwing me off. Any help will be much appreciated, thanks in advance!






calculus matrices numerical-methods gaussian-elimination







share|cite|improve this question









$endgroup$




click here for question



I understand Gaussian elim and the inverse, but am new to Gaussian elim without pivot. Wordiness of the question is also throwing me off. Any help will be much appreciated, thanks in advance!






calculus matrices numerical-methods gaussian-elimination




calculus matrices numerical-methods gaussian-elimination






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 8 '18 at 13:49









RBadgerRBadger

113




113












  • $begingroup$
    You need to find $(I-A)^{-1}$?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 13:52










  • $begingroup$
    Yeah not sure how to do it without pivot
    $endgroup$
    – RBadger
    Mar 8 '18 at 14:20










  • $begingroup$
    First of all, you need to find $B=I-A$. Then, anything you do for finally calculating by GE should also be applied to $I$, then after all steps, you applied to $I$ you will find a matrix that is $(I-A)_{-1}$. Can you take it from here?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:52










  • $begingroup$
    If you need a comprehensive answer, include matrix $A$ in your question here.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:02










  • $begingroup$
    I don’t understand how to get matrix A, I think after I get the matrix I should be okay
    $endgroup$
    – RBadger
    Mar 9 '18 at 13:02


















  • $begingroup$
    You need to find $(I-A)^{-1}$?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 13:52










  • $begingroup$
    Yeah not sure how to do it without pivot
    $endgroup$
    – RBadger
    Mar 8 '18 at 14:20










  • $begingroup$
    First of all, you need to find $B=I-A$. Then, anything you do for finally calculating by GE should also be applied to $I$, then after all steps, you applied to $I$ you will find a matrix that is $(I-A)_{-1}$. Can you take it from here?
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:52










  • $begingroup$
    If you need a comprehensive answer, include matrix $A$ in your question here.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:02










  • $begingroup$
    I don’t understand how to get matrix A, I think after I get the matrix I should be okay
    $endgroup$
    – RBadger
    Mar 9 '18 at 13:02
















$begingroup$
You need to find $(I-A)^{-1}$?
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 13:52




$begingroup$
You need to find $(I-A)^{-1}$?
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 13:52












$begingroup$
Yeah not sure how to do it without pivot
$endgroup$
– RBadger
Mar 8 '18 at 14:20




$begingroup$
Yeah not sure how to do it without pivot
$endgroup$
– RBadger
Mar 8 '18 at 14:20












$begingroup$
First of all, you need to find $B=I-A$. Then, anything you do for finally calculating by GE should also be applied to $I$, then after all steps, you applied to $I$ you will find a matrix that is $(I-A)_{-1}$. Can you take it from here?
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 14:52




$begingroup$
First of all, you need to find $B=I-A$. Then, anything you do for finally calculating by GE should also be applied to $I$, then after all steps, you applied to $I$ you will find a matrix that is $(I-A)_{-1}$. Can you take it from here?
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 14:52












$begingroup$
If you need a comprehensive answer, include matrix $A$ in your question here.
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 15:02




$begingroup$
If you need a comprehensive answer, include matrix $A$ in your question here.
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 15:02












$begingroup$
I don’t understand how to get matrix A, I think after I get the matrix I should be okay
$endgroup$
– RBadger
Mar 9 '18 at 13:02




$begingroup$
I don’t understand how to get matrix A, I think after I get the matrix I should be okay
$endgroup$
– RBadger
Mar 9 '18 at 13:02










1 Answer
1






active

oldest

votes


















1












$begingroup$

Judging from how the question is worded, they seem to ask us not to use a permutation matrix, which in a literal sense means "pivoting" a matrix.



So solving with an A = LU Factorization should suffice. Which would involve working out E = I - A and then finding the inverse, as opposed to the more complete form PA = LU.



There wouldn't be a Gaussian Elimination without pivots, back substitution works on the fundamental idea of having pivots.



I hope that helps.



EDIT:



http://nptel.ac.in/courses/122104019/numerical-analysis/kadalbajoo/lec1/fnode5.html



Here is a small link depicting all three:




  1. No Pivoting.

  2. Partial Pivoting.

  3. Fully Pivoting.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    In the last section of the image, it clearly states gaussian elimination without pivoting.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:49










  • $begingroup$
    @MehrdadZandigohar Yes, just like I am saying "pivoting" a matrix in a more literal way means exchanging rows. The question doesn't want us to "pivot" a matrix partially or fully. "Pivot elements" are called so because of those operations. We commonly refer to them as "pivots" but because of the operations required to find them.
    $endgroup$
    – Shaurya Singh
    Mar 8 '18 at 14:55












  • $begingroup$
    "There wouldn't be a Gaussian Elimination without pivots", that's not true if no diagonal elements are zero in solving steps for the division. You do not need to guess whether pivoting is needed or not when the question clearly states use GE without pivoting unless the question is wrong but it is not.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:59












  • $begingroup$
    I know what pivoting is! You can see here some GE method examples that are solved without pivoting. :) en.wikipedia.org/wiki/Gaussian_elimination
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:10











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1 Answer
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1 Answer
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1












$begingroup$

Judging from how the question is worded, they seem to ask us not to use a permutation matrix, which in a literal sense means "pivoting" a matrix.



So solving with an A = LU Factorization should suffice. Which would involve working out E = I - A and then finding the inverse, as opposed to the more complete form PA = LU.



There wouldn't be a Gaussian Elimination without pivots, back substitution works on the fundamental idea of having pivots.



I hope that helps.



EDIT:



http://nptel.ac.in/courses/122104019/numerical-analysis/kadalbajoo/lec1/fnode5.html



Here is a small link depicting all three:




  1. No Pivoting.

  2. Partial Pivoting.

  3. Fully Pivoting.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    In the last section of the image, it clearly states gaussian elimination without pivoting.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:49










  • $begingroup$
    @MehrdadZandigohar Yes, just like I am saying "pivoting" a matrix in a more literal way means exchanging rows. The question doesn't want us to "pivot" a matrix partially or fully. "Pivot elements" are called so because of those operations. We commonly refer to them as "pivots" but because of the operations required to find them.
    $endgroup$
    – Shaurya Singh
    Mar 8 '18 at 14:55












  • $begingroup$
    "There wouldn't be a Gaussian Elimination without pivots", that's not true if no diagonal elements are zero in solving steps for the division. You do not need to guess whether pivoting is needed or not when the question clearly states use GE without pivoting unless the question is wrong but it is not.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:59












  • $begingroup$
    I know what pivoting is! You can see here some GE method examples that are solved without pivoting. :) en.wikipedia.org/wiki/Gaussian_elimination
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:10
















1












$begingroup$

Judging from how the question is worded, they seem to ask us not to use a permutation matrix, which in a literal sense means "pivoting" a matrix.



So solving with an A = LU Factorization should suffice. Which would involve working out E = I - A and then finding the inverse, as opposed to the more complete form PA = LU.



There wouldn't be a Gaussian Elimination without pivots, back substitution works on the fundamental idea of having pivots.



I hope that helps.



EDIT:



http://nptel.ac.in/courses/122104019/numerical-analysis/kadalbajoo/lec1/fnode5.html



Here is a small link depicting all three:




  1. No Pivoting.

  2. Partial Pivoting.

  3. Fully Pivoting.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    In the last section of the image, it clearly states gaussian elimination without pivoting.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:49










  • $begingroup$
    @MehrdadZandigohar Yes, just like I am saying "pivoting" a matrix in a more literal way means exchanging rows. The question doesn't want us to "pivot" a matrix partially or fully. "Pivot elements" are called so because of those operations. We commonly refer to them as "pivots" but because of the operations required to find them.
    $endgroup$
    – Shaurya Singh
    Mar 8 '18 at 14:55












  • $begingroup$
    "There wouldn't be a Gaussian Elimination without pivots", that's not true if no diagonal elements are zero in solving steps for the division. You do not need to guess whether pivoting is needed or not when the question clearly states use GE without pivoting unless the question is wrong but it is not.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:59












  • $begingroup$
    I know what pivoting is! You can see here some GE method examples that are solved without pivoting. :) en.wikipedia.org/wiki/Gaussian_elimination
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:10














1












1








1





$begingroup$

Judging from how the question is worded, they seem to ask us not to use a permutation matrix, which in a literal sense means "pivoting" a matrix.



So solving with an A = LU Factorization should suffice. Which would involve working out E = I - A and then finding the inverse, as opposed to the more complete form PA = LU.



There wouldn't be a Gaussian Elimination without pivots, back substitution works on the fundamental idea of having pivots.



I hope that helps.



EDIT:



http://nptel.ac.in/courses/122104019/numerical-analysis/kadalbajoo/lec1/fnode5.html



Here is a small link depicting all three:




  1. No Pivoting.

  2. Partial Pivoting.

  3. Fully Pivoting.






share|cite|improve this answer











$endgroup$



Judging from how the question is worded, they seem to ask us not to use a permutation matrix, which in a literal sense means "pivoting" a matrix.



So solving with an A = LU Factorization should suffice. Which would involve working out E = I - A and then finding the inverse, as opposed to the more complete form PA = LU.



There wouldn't be a Gaussian Elimination without pivots, back substitution works on the fundamental idea of having pivots.



I hope that helps.



EDIT:



http://nptel.ac.in/courses/122104019/numerical-analysis/kadalbajoo/lec1/fnode5.html



Here is a small link depicting all three:




  1. No Pivoting.

  2. Partial Pivoting.

  3. Fully Pivoting.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Mar 8 '18 at 15:18

























answered Mar 8 '18 at 14:37









Shaurya SinghShaurya Singh

113




113












  • $begingroup$
    In the last section of the image, it clearly states gaussian elimination without pivoting.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:49










  • $begingroup$
    @MehrdadZandigohar Yes, just like I am saying "pivoting" a matrix in a more literal way means exchanging rows. The question doesn't want us to "pivot" a matrix partially or fully. "Pivot elements" are called so because of those operations. We commonly refer to them as "pivots" but because of the operations required to find them.
    $endgroup$
    – Shaurya Singh
    Mar 8 '18 at 14:55












  • $begingroup$
    "There wouldn't be a Gaussian Elimination without pivots", that's not true if no diagonal elements are zero in solving steps for the division. You do not need to guess whether pivoting is needed or not when the question clearly states use GE without pivoting unless the question is wrong but it is not.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:59












  • $begingroup$
    I know what pivoting is! You can see here some GE method examples that are solved without pivoting. :) en.wikipedia.org/wiki/Gaussian_elimination
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:10


















  • $begingroup$
    In the last section of the image, it clearly states gaussian elimination without pivoting.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:49










  • $begingroup$
    @MehrdadZandigohar Yes, just like I am saying "pivoting" a matrix in a more literal way means exchanging rows. The question doesn't want us to "pivot" a matrix partially or fully. "Pivot elements" are called so because of those operations. We commonly refer to them as "pivots" but because of the operations required to find them.
    $endgroup$
    – Shaurya Singh
    Mar 8 '18 at 14:55












  • $begingroup$
    "There wouldn't be a Gaussian Elimination without pivots", that's not true if no diagonal elements are zero in solving steps for the division. You do not need to guess whether pivoting is needed or not when the question clearly states use GE without pivoting unless the question is wrong but it is not.
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 14:59












  • $begingroup$
    I know what pivoting is! You can see here some GE method examples that are solved without pivoting. :) en.wikipedia.org/wiki/Gaussian_elimination
    $endgroup$
    – Mehrdad Zandigohar
    Mar 8 '18 at 15:10
















$begingroup$
In the last section of the image, it clearly states gaussian elimination without pivoting.
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 14:49




$begingroup$
In the last section of the image, it clearly states gaussian elimination without pivoting.
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 14:49












$begingroup$
@MehrdadZandigohar Yes, just like I am saying "pivoting" a matrix in a more literal way means exchanging rows. The question doesn't want us to "pivot" a matrix partially or fully. "Pivot elements" are called so because of those operations. We commonly refer to them as "pivots" but because of the operations required to find them.
$endgroup$
– Shaurya Singh
Mar 8 '18 at 14:55






$begingroup$
@MehrdadZandigohar Yes, just like I am saying "pivoting" a matrix in a more literal way means exchanging rows. The question doesn't want us to "pivot" a matrix partially or fully. "Pivot elements" are called so because of those operations. We commonly refer to them as "pivots" but because of the operations required to find them.
$endgroup$
– Shaurya Singh
Mar 8 '18 at 14:55














$begingroup$
"There wouldn't be a Gaussian Elimination without pivots", that's not true if no diagonal elements are zero in solving steps for the division. You do not need to guess whether pivoting is needed or not when the question clearly states use GE without pivoting unless the question is wrong but it is not.
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 14:59






$begingroup$
"There wouldn't be a Gaussian Elimination without pivots", that's not true if no diagonal elements are zero in solving steps for the division. You do not need to guess whether pivoting is needed or not when the question clearly states use GE without pivoting unless the question is wrong but it is not.
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 14:59














$begingroup$
I know what pivoting is! You can see here some GE method examples that are solved without pivoting. :) en.wikipedia.org/wiki/Gaussian_elimination
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 15:10




$begingroup$
I know what pivoting is! You can see here some GE method examples that are solved without pivoting. :) en.wikipedia.org/wiki/Gaussian_elimination
$endgroup$
– Mehrdad Zandigohar
Mar 8 '18 at 15:10


















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