Applications of polynomials of a high degree
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What is the highest polynomial degree that has an application in real life, and what is that application? My google search yielded 3rd degree at most.
polynomials applications
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gil_mo
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What is the highest polynomial degree that has an application in real life, and what is that application? My google search yielded 3rd degree at most.
polynomials applications
asked yesterday
gil_mo
62
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gil_mo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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3
This is a fuzzy question, depending on what you call real life. (Many people live without ever using polynomials.) In engineering and scientific circles, higher degree polynomials are certainly in use, with a frequency that decreases with the degree. Mathematicians can play with polynomials of thousands of terms... There is no "highest".
– Yves Daoust
yesterday
Eigenvalue problems in physics can be (informally) considered to be searching for roots of infinite-degree polynomials. Guess it will be hard to find a finite upper bound.
– lisyarus
yesterday
1
Stefan-Boltzmann's law (quartic) must b e a candidate for most frequent actual evaluation of higher-than-cubic polynomial outside formal polynomials and function expansions / transforms.
– Dannie
yesterday
1
@dannie The expression of the Van der Walls forces has a factor in $R^7$.
– Yves Daoust
yesterday
1
@YvesDaoust Lennard-Jones potential has even $R^{12}$.
– lisyarus
yesterday
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What is the highest polynomial degree that has an application in real life, and what is that application? My google search yielded 3rd degree at most.
polynomials applications
asked yesterday
gil_mo
62
New contributor
gil_mo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What is the highest polynomial degree that has an application in real life, and what is that application? My google search yielded 3rd degree at most.
polynomials applications
polynomials applications
asked yesterday
gil_mo
62
New contributor
gil_mo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
gil_mo
62
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gil_mo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
gil_mo
62
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gil_mo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
gil_mo
62
asked yesterday
gil_mo
62
62
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gil_mo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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3
This is a fuzzy question, depending on what you call real life. (Many people live without ever using polynomials.) In engineering and scientific circles, higher degree polynomials are certainly in use, with a frequency that decreases with the degree. Mathematicians can play with polynomials of thousands of terms... There is no "highest".
– Yves Daoust
yesterday
Eigenvalue problems in physics can be (informally) considered to be searching for roots of infinite-degree polynomials. Guess it will be hard to find a finite upper bound.
– lisyarus
yesterday
1
Stefan-Boltzmann's law (quartic) must b e a candidate for most frequent actual evaluation of higher-than-cubic polynomial outside formal polynomials and function expansions / transforms.
– Dannie
yesterday
1
@dannie The expression of the Van der Walls forces has a factor in $R^7$.
– Yves Daoust
yesterday
1
@YvesDaoust Lennard-Jones potential has even $R^{12}$.
– lisyarus
yesterday
add a comment |
3
This is a fuzzy question, depending on what you call real life. (Many people live without ever using polynomials.) In engineering and scientific circles, higher degree polynomials are certainly in use, with a frequency that decreases with the degree. Mathematicians can play with polynomials of thousands of terms... There is no "highest".
– Yves Daoust
yesterday
Eigenvalue problems in physics can be (informally) considered to be searching for roots of infinite-degree polynomials. Guess it will be hard to find a finite upper bound.
– lisyarus
yesterday
1
Stefan-Boltzmann's law (quartic) must b e a candidate for most frequent actual evaluation of higher-than-cubic polynomial outside formal polynomials and function expansions / transforms.
– Dannie
yesterday
1
@dannie The expression of the Van der Walls forces has a factor in $R^7$.
– Yves Daoust
yesterday
1
@YvesDaoust Lennard-Jones potential has even $R^{12}$.
– lisyarus
yesterday
3
3
This is a fuzzy question, depending on what you call real life. (Many people live without ever using polynomials.) In engineering and scientific circles, higher degree polynomials are certainly in use, with a frequency that decreases with the degree. Mathematicians can play with polynomials of thousands of terms... There is no "highest".
– Yves Daoust
yesterday
This is a fuzzy question, depending on what you call real life. (Many people live without ever using polynomials.) In engineering and scientific circles, higher degree polynomials are certainly in use, with a frequency that decreases with the degree. Mathematicians can play with polynomials of thousands of terms... There is no "highest".
– Yves Daoust
yesterday
Eigenvalue problems in physics can be (informally) considered to be searching for roots of infinite-degree polynomials. Guess it will be hard to find a finite upper bound.
– lisyarus
yesterday
Eigenvalue problems in physics can be (informally) considered to be searching for roots of infinite-degree polynomials. Guess it will be hard to find a finite upper bound.
– lisyarus
yesterday
1
1
Stefan-Boltzmann's law (quartic) must b e a candidate for most frequent actual evaluation of higher-than-cubic polynomial outside formal polynomials and function expansions / transforms.
– Dannie
yesterday
Stefan-Boltzmann's law (quartic) must b e a candidate for most frequent actual evaluation of higher-than-cubic polynomial outside formal polynomials and function expansions / transforms.
– Dannie
yesterday
1
1
@dannie The expression of the Van der Walls forces has a factor in $R^7$.
– Yves Daoust
yesterday
@dannie The expression of the Van der Walls forces has a factor in $R^7$.
– Yves Daoust
yesterday
1
1
@YvesDaoust Lennard-Jones potential has even $R^{12}$.
– lisyarus
yesterday
@YvesDaoust Lennard-Jones potential has even $R^{12}$.
– lisyarus
yesterday
add a comment |
2 Answers
2
active
oldest
votes
up vote
3
down vote
accepted
Practitioners in signal and image processing heavily use the so-called Discrete Fourier Transform, which is a polynomial evaluated on complex variables. Applications in medical imaging abound.
The degree of these polynomials typically reaches the image size, which can be like 4096 or much more.
Other consumers of polynomials are the error correction methods (such as those used in digital communication or CD readers). They are implemented in some types of barcodes, with degrees that reach dozens. If I am right, the QR codes use up to degree 69.
answered yesterday
Yves Daoust
122k668217
A good one. IIRC the error correcting code used in CDs uses polynomials up to degree 28.
– Jyrki Lahtonen
yesterday
add a comment |
up vote
1
down vote
The characteristic polynomial of any matrix (though rarely explicitly computed) gives quite a bit of information about that matrix that is incredibly useful in a huge variety of data analysis settings (machine learning, dimensionality reduction, etc.) The degree of this polynomial is the same as the size of the matrix (depending on setting, this can easily be in the multiple thousands, or even larger). Admittedly this is more of a computer science answer than math, but is still relevant.
answered yesterday
DreamConspiracy
8711216
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Practitioners in signal and image processing heavily use the so-called Discrete Fourier Transform, which is a polynomial evaluated on complex variables. Applications in medical imaging abound.
The degree of these polynomials typically reaches the image size, which can be like 4096 or much more.
Other consumers of polynomials are the error correction methods (such as those used in digital communication or CD readers). They are implemented in some types of barcodes, with degrees that reach dozens. If I am right, the QR codes use up to degree 69.
answered yesterday
Yves Daoust
122k668217
A good one. IIRC the error correcting code used in CDs uses polynomials up to degree 28.
– Jyrki Lahtonen
yesterday
add a comment |
up vote
3
down vote
accepted
Practitioners in signal and image processing heavily use the so-called Discrete Fourier Transform, which is a polynomial evaluated on complex variables. Applications in medical imaging abound.
The degree of these polynomials typically reaches the image size, which can be like 4096 or much more.
Other consumers of polynomials are the error correction methods (such as those used in digital communication or CD readers). They are implemented in some types of barcodes, with degrees that reach dozens. If I am right, the QR codes use up to degree 69.
answered yesterday
Yves Daoust
122k668217
A good one. IIRC the error correcting code used in CDs uses polynomials up to degree 28.
– Jyrki Lahtonen
yesterday
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Practitioners in signal and image processing heavily use the so-called Discrete Fourier Transform, which is a polynomial evaluated on complex variables. Applications in medical imaging abound.
The degree of these polynomials typically reaches the image size, which can be like 4096 or much more.
Other consumers of polynomials are the error correction methods (such as those used in digital communication or CD readers). They are implemented in some types of barcodes, with degrees that reach dozens. If I am right, the QR codes use up to degree 69.
answered yesterday
Yves Daoust
122k668217
Practitioners in signal and image processing heavily use the so-called Discrete Fourier Transform, which is a polynomial evaluated on complex variables. Applications in medical imaging abound.
The degree of these polynomials typically reaches the image size, which can be like 4096 or much more.
Other consumers of polynomials are the error correction methods (such as those used in digital communication or CD readers). They are implemented in some types of barcodes, with degrees that reach dozens. If I am right, the QR codes use up to degree 69.
answered yesterday
Yves Daoust
122k668217
edited yesterday
answered yesterday
Yves Daoust
122k668217
answered yesterday
Yves Daoust
122k668217
answered yesterday
Yves Daoust
122k668217
122k668217
A good one. IIRC the error correcting code used in CDs uses polynomials up to degree 28.
– Jyrki Lahtonen
yesterday
add a comment |
A good one. IIRC the error correcting code used in CDs uses polynomials up to degree 28.
– Jyrki Lahtonen
yesterday
A good one. IIRC the error correcting code used in CDs uses polynomials up to degree 28.
– Jyrki Lahtonen
yesterday
A good one. IIRC the error correcting code used in CDs uses polynomials up to degree 28.
– Jyrki Lahtonen
yesterday
add a comment |
up vote
1
down vote
The characteristic polynomial of any matrix (though rarely explicitly computed) gives quite a bit of information about that matrix that is incredibly useful in a huge variety of data analysis settings (machine learning, dimensionality reduction, etc.) The degree of this polynomial is the same as the size of the matrix (depending on setting, this can easily be in the multiple thousands, or even larger). Admittedly this is more of a computer science answer than math, but is still relevant.
answered yesterday
DreamConspiracy
8711216
add a comment |
up vote
1
down vote
The characteristic polynomial of any matrix (though rarely explicitly computed) gives quite a bit of information about that matrix that is incredibly useful in a huge variety of data analysis settings (machine learning, dimensionality reduction, etc.) The degree of this polynomial is the same as the size of the matrix (depending on setting, this can easily be in the multiple thousands, or even larger). Admittedly this is more of a computer science answer than math, but is still relevant.
answered yesterday
DreamConspiracy
8711216
add a comment |
up vote
1
down vote
up vote
1
down vote
The characteristic polynomial of any matrix (though rarely explicitly computed) gives quite a bit of information about that matrix that is incredibly useful in a huge variety of data analysis settings (machine learning, dimensionality reduction, etc.) The degree of this polynomial is the same as the size of the matrix (depending on setting, this can easily be in the multiple thousands, or even larger). Admittedly this is more of a computer science answer than math, but is still relevant.
answered yesterday
DreamConspiracy
8711216
The characteristic polynomial of any matrix (though rarely explicitly computed) gives quite a bit of information about that matrix that is incredibly useful in a huge variety of data analysis settings (machine learning, dimensionality reduction, etc.) The degree of this polynomial is the same as the size of the matrix (depending on setting, this can easily be in the multiple thousands, or even larger). Admittedly this is more of a computer science answer than math, but is still relevant.
answered yesterday
DreamConspiracy
8711216
answered yesterday
DreamConspiracy
8711216
answered yesterday
DreamConspiracy
8711216
answered yesterday
DreamConspiracy
8711216
8711216
add a comment |
add a comment |
gil_mo is a new contributor. Be nice, and check out our Code of Conduct.
gil_mo is a new contributor. Be nice, and check out our Code of Conduct.
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3
This is a fuzzy question, depending on what you call real life. (Many people live without ever using polynomials.) In engineering and scientific circles, higher degree polynomials are certainly in use, with a frequency that decreases with the degree. Mathematicians can play with polynomials of thousands of terms... There is no "highest".
– Yves Daoust
yesterday
Eigenvalue problems in physics can be (informally) considered to be searching for roots of infinite-degree polynomials. Guess it will be hard to find a finite upper bound.
– lisyarus
yesterday
1
Stefan-Boltzmann's law (quartic) must b e a candidate for most frequent actual evaluation of higher-than-cubic polynomial outside formal polynomials and function expansions / transforms.
– Dannie
yesterday
1
@dannie The expression of the Van der Walls forces has a factor in $R^7$.
– Yves Daoust
yesterday
1
@YvesDaoust Lennard-Jones potential has even $R^{12}$.
– lisyarus
yesterday