Sparse matrix computational difficulties

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I am a computer science student. But I start writing here because my problem is not code related. It is purely computational related.



I am trying to calculated inverse of a large (e.g., $2000 times 2000$) square matrix. This matrix is band diagonal matrix.



The non zero elements are very small numbers (e.g: $1--6$). They never exceed 6.



Now when I invert this matrix the result of inversion are all same number displayed.



Output:



9.711E013 9.711E013 9.711E013 9.711E013....................
9.711E013 9.711E013 9.711E013 9.711E013......................

9.711E013 9.711E013 9.711E013 9.711E013.....................
..............................................................

 9.711E013 9.711E013 9.711E013 9.711E013


My question is that why this type of output I get? What is the mathematical reason behind this?




matrix-equations matrix-decomposition singularity-theory sparse-matrices




share|cite|improve this question

















  • 1




    what are you using to invert it? Matlab, for example, should be easily inverting this.
    – dezdichado
    yesterday










  • I am using universal java matrix package for matrix inversion. I write down this code in java.
    – Ellena Mori
    yesterday










  • You should post your code, I don't think we have enough information to see what's going wrong.
    – littleO
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link.
    – Ellena Mori
    yesterday














up vote
2
down vote

favorite
1












I am a computer science student. But I start writing here because my problem is not code related. It is purely computational related.



I am trying to calculated inverse of a large (e.g., $2000 times 2000$) square matrix. This matrix is band diagonal matrix.



The non zero elements are very small numbers (e.g: $1--6$). They never exceed 6.



Now when I invert this matrix the result of inversion are all same number displayed.



Output:



9.711E013 9.711E013 9.711E013 9.711E013....................
9.711E013 9.711E013 9.711E013 9.711E013......................

9.711E013 9.711E013 9.711E013 9.711E013.....................
..............................................................

 9.711E013 9.711E013 9.711E013 9.711E013


My question is that why this type of output I get? What is the mathematical reason behind this?




matrix-equations matrix-decomposition singularity-theory sparse-matrices




share|cite|improve this question

















  • 1




    what are you using to invert it? Matlab, for example, should be easily inverting this.
    – dezdichado
    yesterday










  • I am using universal java matrix package for matrix inversion. I write down this code in java.
    – Ellena Mori
    yesterday










  • You should post your code, I don't think we have enough information to see what's going wrong.
    – littleO
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link.
    – Ellena Mori
    yesterday












up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





I am a computer science student. But I start writing here because my problem is not code related. It is purely computational related.



I am trying to calculated inverse of a large (e.g., $2000 times 2000$) square matrix. This matrix is band diagonal matrix.



The non zero elements are very small numbers (e.g: $1--6$). They never exceed 6.



Now when I invert this matrix the result of inversion are all same number displayed.



Output:



9.711E013 9.711E013 9.711E013 9.711E013....................
9.711E013 9.711E013 9.711E013 9.711E013......................

9.711E013 9.711E013 9.711E013 9.711E013.....................
..............................................................

 9.711E013 9.711E013 9.711E013 9.711E013


My question is that why this type of output I get? What is the mathematical reason behind this?




matrix-equations matrix-decomposition singularity-theory sparse-matrices




share|cite|improve this question













I am a computer science student. But I start writing here because my problem is not code related. It is purely computational related.



I am trying to calculated inverse of a large (e.g., $2000 times 2000$) square matrix. This matrix is band diagonal matrix.



The non zero elements are very small numbers (e.g: $1--6$). They never exceed 6.



Now when I invert this matrix the result of inversion are all same number displayed.



Output:



9.711E013 9.711E013 9.711E013 9.711E013....................
9.711E013 9.711E013 9.711E013 9.711E013......................

9.711E013 9.711E013 9.711E013 9.711E013.....................
..............................................................

 9.711E013 9.711E013 9.711E013 9.711E013


My question is that why this type of output I get? What is the mathematical reason behind this?





matrix-equations matrix-decomposition singularity-theory sparse-matrices





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited yesterday









David G. Stork

7,3102728




7,3102728









asked yesterday









Ellena Mori

132




132







  • 1




    what are you using to invert it? Matlab, for example, should be easily inverting this.
    – dezdichado
    yesterday










  • I am using universal java matrix package for matrix inversion. I write down this code in java.
    – Ellena Mori
    yesterday










  • You should post your code, I don't think we have enough information to see what's going wrong.
    – littleO
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link.
    – Ellena Mori
    yesterday












  • 1




    what are you using to invert it? Matlab, for example, should be easily inverting this.
    – dezdichado
    yesterday










  • I am using universal java matrix package for matrix inversion. I write down this code in java.
    – Ellena Mori
    yesterday










  • You should post your code, I don't think we have enough information to see what's going wrong.
    – littleO
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link.
    – Ellena Mori
    yesterday







1




1




what are you using to invert it? Matlab, for example, should be easily inverting this.
– dezdichado
yesterday




what are you using to invert it? Matlab, for example, should be easily inverting this.
– dezdichado
yesterday












I am using universal java matrix package for matrix inversion. I write down this code in java.
– Ellena Mori
yesterday




I am using universal java matrix package for matrix inversion. I write down this code in java.
– Ellena Mori
yesterday












You should post your code, I don't think we have enough information to see what's going wrong.
– littleO
yesterday




You should post your code, I don't think we have enough information to see what's going wrong.
– littleO
yesterday












math.stackexchange.com/questions/2872771/… Please go through this link.
– Ellena Mori
yesterday




math.stackexchange.com/questions/2872771/… Please go through this link.
– Ellena Mori
yesterday










1 Answer
1






active

oldest

votes

















up vote
0
down vote



accepted










EDITED: thanks to comment of copper.hat.



The mathematical/numerical reason is that the condition number defined as
$$
varkappa(A) = fracsigma_max(A)sigma_min(A)
$$
is too large, say of order $10^10$ or even more. $sigma_min, max(A)$ is the minimal and maximal singular values of matrix $A$.



The case of small determinant is a particular case and in some cases implied from the argument above.






share|cite|improve this answer























  • This doesn't explain why all the entries in the output are the same, though.
    – littleO
    yesterday










  • My guess would be that this number is the “infinity” of used software.
    – pointguard0
    yesterday











  • I used intellj idea to write down java code and use universal java matrix package to invert this matrix.
    – Ellena Mori
    yesterday






  • 2




    A small determinant does not necessarily translate into ill conditioned. Generally the issue is because the condition number is large, which is related to the singular values, not the eigenvalues.
    – copper.hat
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link where I explain my code.
    – Ellena Mori
    yesterday










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1 Answer
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active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote



accepted










EDITED: thanks to comment of copper.hat.



The mathematical/numerical reason is that the condition number defined as
$$
varkappa(A) = fracsigma_max(A)sigma_min(A)
$$
is too large, say of order $10^10$ or even more. $sigma_min, max(A)$ is the minimal and maximal singular values of matrix $A$.



The case of small determinant is a particular case and in some cases implied from the argument above.






share|cite|improve this answer























  • This doesn't explain why all the entries in the output are the same, though.
    – littleO
    yesterday










  • My guess would be that this number is the “infinity” of used software.
    – pointguard0
    yesterday











  • I used intellj idea to write down java code and use universal java matrix package to invert this matrix.
    – Ellena Mori
    yesterday






  • 2




    A small determinant does not necessarily translate into ill conditioned. Generally the issue is because the condition number is large, which is related to the singular values, not the eigenvalues.
    – copper.hat
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link where I explain my code.
    – Ellena Mori
    yesterday














up vote
0
down vote



accepted










EDITED: thanks to comment of copper.hat.



The mathematical/numerical reason is that the condition number defined as
$$
varkappa(A) = fracsigma_max(A)sigma_min(A)
$$
is too large, say of order $10^10$ or even more. $sigma_min, max(A)$ is the minimal and maximal singular values of matrix $A$.



The case of small determinant is a particular case and in some cases implied from the argument above.






share|cite|improve this answer























  • This doesn't explain why all the entries in the output are the same, though.
    – littleO
    yesterday










  • My guess would be that this number is the “infinity” of used software.
    – pointguard0
    yesterday











  • I used intellj idea to write down java code and use universal java matrix package to invert this matrix.
    – Ellena Mori
    yesterday






  • 2




    A small determinant does not necessarily translate into ill conditioned. Generally the issue is because the condition number is large, which is related to the singular values, not the eigenvalues.
    – copper.hat
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link where I explain my code.
    – Ellena Mori
    yesterday












up vote
0
down vote



accepted







up vote
0
down vote



accepted






EDITED: thanks to comment of copper.hat.



The mathematical/numerical reason is that the condition number defined as
$$
varkappa(A) = fracsigma_max(A)sigma_min(A)
$$
is too large, say of order $10^10$ or even more. $sigma_min, max(A)$ is the minimal and maximal singular values of matrix $A$.



The case of small determinant is a particular case and in some cases implied from the argument above.






share|cite|improve this answer















EDITED: thanks to comment of copper.hat.



The mathematical/numerical reason is that the condition number defined as
$$
varkappa(A) = fracsigma_max(A)sigma_min(A)
$$
is too large, say of order $10^10$ or even more. $sigma_min, max(A)$ is the minimal and maximal singular values of matrix $A$.



The case of small determinant is a particular case and in some cases implied from the argument above.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited yesterday


























answered yesterday









pointguard0

514215




514215











  • This doesn't explain why all the entries in the output are the same, though.
    – littleO
    yesterday










  • My guess would be that this number is the “infinity” of used software.
    – pointguard0
    yesterday











  • I used intellj idea to write down java code and use universal java matrix package to invert this matrix.
    – Ellena Mori
    yesterday






  • 2




    A small determinant does not necessarily translate into ill conditioned. Generally the issue is because the condition number is large, which is related to the singular values, not the eigenvalues.
    – copper.hat
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link where I explain my code.
    – Ellena Mori
    yesterday
















  • This doesn't explain why all the entries in the output are the same, though.
    – littleO
    yesterday










  • My guess would be that this number is the “infinity” of used software.
    – pointguard0
    yesterday











  • I used intellj idea to write down java code and use universal java matrix package to invert this matrix.
    – Ellena Mori
    yesterday






  • 2




    A small determinant does not necessarily translate into ill conditioned. Generally the issue is because the condition number is large, which is related to the singular values, not the eigenvalues.
    – copper.hat
    yesterday










  • math.stackexchange.com/questions/2872771/… Please go through this link where I explain my code.
    – Ellena Mori
    yesterday















This doesn't explain why all the entries in the output are the same, though.
– littleO
yesterday




This doesn't explain why all the entries in the output are the same, though.
– littleO
yesterday












My guess would be that this number is the “infinity” of used software.
– pointguard0
yesterday





My guess would be that this number is the “infinity” of used software.
– pointguard0
yesterday













I used intellj idea to write down java code and use universal java matrix package to invert this matrix.
– Ellena Mori
yesterday




I used intellj idea to write down java code and use universal java matrix package to invert this matrix.
– Ellena Mori
yesterday




2




2




A small determinant does not necessarily translate into ill conditioned. Generally the issue is because the condition number is large, which is related to the singular values, not the eigenvalues.
– copper.hat
yesterday




A small determinant does not necessarily translate into ill conditioned. Generally the issue is because the condition number is large, which is related to the singular values, not the eigenvalues.
– copper.hat
yesterday












math.stackexchange.com/questions/2872771/… Please go through this link where I explain my code.
– Ellena Mori
yesterday




math.stackexchange.com/questions/2872771/… Please go through this link where I explain my code.
– Ellena Mori
yesterday












 

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