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Applications of polynomial systems of equations
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What are some applications of Polynomial Systems of Equations?
I am doing a project with Artificial Neural Networks where I use standard ANNs with a different backpropagation algorithm to find solutions of a SOPE.
polynomials soft-question systems-of-equations
edited Jul 30 at 20:23
Rodrigo de Azevedo
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asked Jul 30 at 19:57
Shrey Joshi
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up vote
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favorite
1
What are some applications of Polynomial Systems of Equations?
I am doing a project with Artificial Neural Networks where I use standard ANNs with a different backpropagation algorithm to find solutions of a SOPE.
polynomials soft-question systems-of-equations
edited Jul 30 at 20:23
Rodrigo de Azevedo
12.6k41751
asked Jul 30 at 19:57
Shrey Joshi
1349
For example, deciding whether a given graph is $2$-colorable can be reduced to deciding whether a system of linear and quadratic equations is feasible. You may want to take a look at Expressing Combinatorial Optimization Problems by Systems of Polynomial Equations and the Nullstellensatz (2007).
– Rodrigo de Azevedo
Jul 30 at 20:28
add a comment |Â
up vote
2
down vote
favorite
1
up vote
2
down vote
favorite
1
1
What are some applications of Polynomial Systems of Equations?
I am doing a project with Artificial Neural Networks where I use standard ANNs with a different backpropagation algorithm to find solutions of a SOPE.
polynomials soft-question systems-of-equations
edited Jul 30 at 20:23
Rodrigo de Azevedo
12.6k41751
asked Jul 30 at 19:57
Shrey Joshi
1349
What are some applications of Polynomial Systems of Equations?
I am doing a project with Artificial Neural Networks where I use standard ANNs with a different backpropagation algorithm to find solutions of a SOPE.
polynomials soft-question systems-of-equations
edited Jul 30 at 20:23
Rodrigo de Azevedo
12.6k41751
asked Jul 30 at 19:57
Shrey Joshi
1349
edited Jul 30 at 20:23
Rodrigo de Azevedo
12.6k41751
edited Jul 30 at 20:23
Rodrigo de Azevedo
12.6k41751
edited Jul 30 at 20:23
Rodrigo de Azevedo
12.6k41751
12.6k41751
asked Jul 30 at 19:57
Shrey Joshi
1349
asked Jul 30 at 19:57
Shrey Joshi
1349
asked Jul 30 at 19:57
Shrey Joshi
1349
1349
For example, deciding whether a given graph is $2$-colorable can be reduced to deciding whether a system of linear and quadratic equations is feasible. You may want to take a look at Expressing Combinatorial Optimization Problems by Systems of Polynomial Equations and the Nullstellensatz (2007).
– Rodrigo de Azevedo
Jul 30 at 20:28
add a comment |Â
For example, deciding whether a given graph is $2$-colorable can be reduced to deciding whether a system of linear and quadratic equations is feasible. You may want to take a look at Expressing Combinatorial Optimization Problems by Systems of Polynomial Equations and the Nullstellensatz (2007).
– Rodrigo de Azevedo
Jul 30 at 20:28
For example, deciding whether a given graph is $2$-colorable can be reduced to deciding whether a system of linear and quadratic equations is feasible. You may want to take a look at Expressing Combinatorial Optimization Problems by Systems of Polynomial Equations and the Nullstellensatz (2007).
– Rodrigo de Azevedo
Jul 30 at 20:28
For example, deciding whether a given graph is $2$-colorable can be reduced to deciding whether a system of linear and quadratic equations is feasible. You may want to take a look at Expressing Combinatorial Optimization Problems by Systems of Polynomial Equations and the Nullstellensatz (2007).
– Rodrigo de Azevedo
Jul 30 at 20:28
add a comment |Â
1 Answer
1
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oldest
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up vote
0
down vote
Computing tensor rank decomposition is currently a quite hot topic in the numerical linear algebra community and involve solving systems of polynomial equations. In short, the tensor rank decomposition can be seen as an SVD decomposition but for "matrices" with more than 2 indices.
answered Jul 30 at 20:08
Surb
36.2k84274
Thanks for your answer, I also know there is some sort of application in neuro-physiology, I don't know exactly what it does though.
– Shrey Joshi
Jul 30 at 20:17
well computing tensor decompositions have a lot of applications for instance solving large scale PDEs, machine learning, signal processing, quantum physics, etc. Although already quite old for the field, this survey gives some interesting references: epubs.siam.org/doi/pdf/10.1137/07070111X
– Surb
Jul 30 at 20:32
By the way, do you have a paper/preprint about your work?
– Surb
Jul 30 at 20:34
Is there a more straightforward real world application of this? Something the people outside the mathematical community would care about?
– Shrey Joshi
Jul 31 at 19:50
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Computing tensor rank decomposition is currently a quite hot topic in the numerical linear algebra community and involve solving systems of polynomial equations. In short, the tensor rank decomposition can be seen as an SVD decomposition but for "matrices" with more than 2 indices.
answered Jul 30 at 20:08
Surb
36.2k84274
Thanks for your answer, I also know there is some sort of application in neuro-physiology, I don't know exactly what it does though.
– Shrey Joshi
Jul 30 at 20:17
well computing tensor decompositions have a lot of applications for instance solving large scale PDEs, machine learning, signal processing, quantum physics, etc. Although already quite old for the field, this survey gives some interesting references: epubs.siam.org/doi/pdf/10.1137/07070111X
– Surb
Jul 30 at 20:32
By the way, do you have a paper/preprint about your work?
– Surb
Jul 30 at 20:34
Is there a more straightforward real world application of this? Something the people outside the mathematical community would care about?
– Shrey Joshi
Jul 31 at 19:50
add a comment |Â
up vote
0
down vote
Computing tensor rank decomposition is currently a quite hot topic in the numerical linear algebra community and involve solving systems of polynomial equations. In short, the tensor rank decomposition can be seen as an SVD decomposition but for "matrices" with more than 2 indices.
answered Jul 30 at 20:08
Surb
36.2k84274
Thanks for your answer, I also know there is some sort of application in neuro-physiology, I don't know exactly what it does though.
– Shrey Joshi
Jul 30 at 20:17
well computing tensor decompositions have a lot of applications for instance solving large scale PDEs, machine learning, signal processing, quantum physics, etc. Although already quite old for the field, this survey gives some interesting references: epubs.siam.org/doi/pdf/10.1137/07070111X
– Surb
Jul 30 at 20:32
By the way, do you have a paper/preprint about your work?
– Surb
Jul 30 at 20:34
Is there a more straightforward real world application of this? Something the people outside the mathematical community would care about?
– Shrey Joshi
Jul 31 at 19:50
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Computing tensor rank decomposition is currently a quite hot topic in the numerical linear algebra community and involve solving systems of polynomial equations. In short, the tensor rank decomposition can be seen as an SVD decomposition but for "matrices" with more than 2 indices.
answered Jul 30 at 20:08
Surb
36.2k84274
Computing tensor rank decomposition is currently a quite hot topic in the numerical linear algebra community and involve solving systems of polynomial equations. In short, the tensor rank decomposition can be seen as an SVD decomposition but for "matrices" with more than 2 indices.
answered Jul 30 at 20:08
Surb
36.2k84274
answered Jul 30 at 20:08
Surb
36.2k84274
answered Jul 30 at 20:08
Surb
36.2k84274
answered Jul 30 at 20:08
Surb
36.2k84274
36.2k84274
Thanks for your answer, I also know there is some sort of application in neuro-physiology, I don't know exactly what it does though.
– Shrey Joshi
Jul 30 at 20:17
well computing tensor decompositions have a lot of applications for instance solving large scale PDEs, machine learning, signal processing, quantum physics, etc. Although already quite old for the field, this survey gives some interesting references: epubs.siam.org/doi/pdf/10.1137/07070111X
– Surb
Jul 30 at 20:32
By the way, do you have a paper/preprint about your work?
– Surb
Jul 30 at 20:34
Is there a more straightforward real world application of this? Something the people outside the mathematical community would care about?
– Shrey Joshi
Jul 31 at 19:50
add a comment |Â
Thanks for your answer, I also know there is some sort of application in neuro-physiology, I don't know exactly what it does though.
– Shrey Joshi
Jul 30 at 20:17
well computing tensor decompositions have a lot of applications for instance solving large scale PDEs, machine learning, signal processing, quantum physics, etc. Although already quite old for the field, this survey gives some interesting references: epubs.siam.org/doi/pdf/10.1137/07070111X
– Surb
Jul 30 at 20:32
By the way, do you have a paper/preprint about your work?
– Surb
Jul 30 at 20:34
Is there a more straightforward real world application of this? Something the people outside the mathematical community would care about?
– Shrey Joshi
Jul 31 at 19:50
Thanks for your answer, I also know there is some sort of application in neuro-physiology, I don't know exactly what it does though.
– Shrey Joshi
Jul 30 at 20:17
Thanks for your answer, I also know there is some sort of application in neuro-physiology, I don't know exactly what it does though.
– Shrey Joshi
Jul 30 at 20:17
well computing tensor decompositions have a lot of applications for instance solving large scale PDEs, machine learning, signal processing, quantum physics, etc. Although already quite old for the field, this survey gives some interesting references: epubs.siam.org/doi/pdf/10.1137/07070111X
– Surb
Jul 30 at 20:32
well computing tensor decompositions have a lot of applications for instance solving large scale PDEs, machine learning, signal processing, quantum physics, etc. Although already quite old for the field, this survey gives some interesting references: epubs.siam.org/doi/pdf/10.1137/07070111X
– Surb
Jul 30 at 20:32
By the way, do you have a paper/preprint about your work?
– Surb
Jul 30 at 20:34
By the way, do you have a paper/preprint about your work?
– Surb
Jul 30 at 20:34
Is there a more straightforward real world application of this? Something the people outside the mathematical community would care about?
– Shrey Joshi
Jul 31 at 19:50
Is there a more straightforward real world application of this? Something the people outside the mathematical community would care about?
– Shrey Joshi
Jul 31 at 19:50
add a comment |Â
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For example, deciding whether a given graph is $2$-colorable can be reduced to deciding whether a system of linear and quadratic equations is feasible. You may want to take a look at Expressing Combinatorial Optimization Problems by Systems of Polynomial Equations and the Nullstellensatz (2007).
– Rodrigo de Azevedo
Jul 30 at 20:28