What is the definition of spectral convergence? The 2019 Stack Overflow Developer Survey Results Are InOptimal method to numerically integrate a spectral distribution dataGauss–Seidel and Jacobi methods convergenceSpectral radius of $A$ and convergence of $A^k$Newtons Method, Multiplicity, and Rates of ConvergenceWhat is the convergence rate of Brent's method (root-finding algorithm)?Definition of Global ConvergenceLearning spectral methods in numerical analysisIterative methods: What happens when the spectral radius of a matrix is exactly 1?Iteration matrix and convergenceSpeed of Eigenvalue Solver Convergence with Different Spectral Shifts
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What is the definition of spectral convergence?
The 2019 Stack Overflow Developer Survey Results Are InOptimal method to numerically integrate a spectral distribution dataGauss–Seidel and Jacobi methods convergenceSpectral radius of $A$ and convergence of $A^k$Newtons Method, Multiplicity, and Rates of ConvergenceWhat is the convergence rate of Brent's method (root-finding algorithm)?Definition of Global ConvergenceLearning spectral methods in numerical analysisIterative methods: What happens when the spectral radius of a matrix is exactly 1?Iteration matrix and convergenceSpeed of Eigenvalue Solver Convergence with Different Spectral Shifts
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I don't understand what is spectral convergence. The definitions I found in google are very physics. Is there any definition in mathematics ?
numerical-methods
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
$endgroup$
add a comment |
$begingroup$
I don't understand what is spectral convergence. The definitions I found in google are very physics. Is there any definition in mathematics ?
numerical-methods
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
$endgroup$
$begingroup$
Don't know, but there are mentions here: math.stackexchange.com/search?q=%22spectral+convergence%22
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– Keith McClary
Nov 5 '18 at 6:23
add a comment |
$begingroup$
I don't understand what is spectral convergence. The definitions I found in google are very physics. Is there any definition in mathematics ?
numerical-methods
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
$endgroup$
I don't understand what is spectral convergence. The definitions I found in google are very physics. Is there any definition in mathematics ?
numerical-methods
numerical-methods
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
asked Nov 5 '18 at 5:29
Haiyi TanHaiyi Tan
354
354
$begingroup$
Don't know, but there are mentions here: math.stackexchange.com/search?q=%22spectral+convergence%22
$endgroup$
– Keith McClary
Nov 5 '18 at 6:23
add a comment |
$begingroup$
Don't know, but there are mentions here: math.stackexchange.com/search?q=%22spectral+convergence%22
$endgroup$
– Keith McClary
Nov 5 '18 at 6:23
$begingroup$
Don't know, but there are mentions here: math.stackexchange.com/search?q=%22spectral+convergence%22
$endgroup$
– Keith McClary
Nov 5 '18 at 6:23
$begingroup$
Don't know, but there are mentions here: math.stackexchange.com/search?q=%22spectral+convergence%22
$endgroup$
– Keith McClary
Nov 5 '18 at 6:23
add a comment |
1 Answer
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This is quoted from an online article:
Spectral convergence means that the error with increasing resolution (number of grid points $N$) is in fact decreasing exponentially, $propto (L/N)^N$, as opposed to algebraically, $propto (L/N)^p$ as for finite-difference methods.
[ I remember finding a description in some textbook in the library, will update when I get it next time ]
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
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add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
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votes
$begingroup$
This is quoted from an online article:
Spectral convergence means that the error with increasing resolution (number of grid points $N$) is in fact decreasing exponentially, $propto (L/N)^N$, as opposed to algebraically, $propto (L/N)^p$ as for finite-difference methods.
[ I remember finding a description in some textbook in the library, will update when I get it next time ]
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
$endgroup$
add a comment |
$begingroup$
This is quoted from an online article:
Spectral convergence means that the error with increasing resolution (number of grid points $N$) is in fact decreasing exponentially, $propto (L/N)^N$, as opposed to algebraically, $propto (L/N)^p$ as for finite-difference methods.
[ I remember finding a description in some textbook in the library, will update when I get it next time ]
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
$endgroup$
add a comment |
$begingroup$
This is quoted from an online article:
Spectral convergence means that the error with increasing resolution (number of grid points $N$) is in fact decreasing exponentially, $propto (L/N)^N$, as opposed to algebraically, $propto (L/N)^p$ as for finite-difference methods.
[ I remember finding a description in some textbook in the library, will update when I get it next time ]
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
$endgroup$
This is quoted from an online article:
Spectral convergence means that the error with increasing resolution (number of grid points $N$) is in fact decreasing exponentially, $propto (L/N)^N$, as opposed to algebraically, $propto (L/N)^p$ as for finite-difference methods.
[ I remember finding a description in some textbook in the library, will update when I get it next time ]
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
answered Mar 24 at 7:19
Yan King YinYan King Yin
466211
466211
add a comment |
add a comment |
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Don't know, but there are mentions here: math.stackexchange.com/search?q=%22spectral+convergence%22
$endgroup$
– Keith McClary
Nov 5 '18 at 6:23