Difference between revisions of "Tikhoind.m"
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{{DISPLAYTITLE:tikhoind.m}} __NOTOC__ | {{DISPLAYTITLE:tikhoind.m}} __NOTOC__ | ||
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Analytical Tikhonov regularised solution to K*x=y without any constraints (indeterminate output). | Analytical Tikhonov regularised solution to K*x=y without any constraints (indeterminate output). | ||
==Syntax== | ==Syntax== | ||
| − | [x,err,reg]=tikhoind(K,D,y,lam) | + | [x,err,reg]=tikhoind(K,D,y,lam) |
==Arguments== | ==Arguments== | ||
| − | K - kernel matrix, may be complex, may be non-square | + | K - kernel matrix, may be complex, may be non-square |
D - regularisation matrix, leave empty to use finite | D - regularisation matrix, leave empty to use finite | ||
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==Outputs== | ==Outputs== | ||
| − | x - a real vector, a minimum of | + | x - a real vector, a minimum of |
norm(K*x-y,2)^2+lambda*norm(D*x,2)^2 | norm(K*x-y,2)^2+lambda*norm(D*x,2)^2 | ||
| − | + | ||
err - error signal norm(K*x-y,2)^2 | err - error signal norm(K*x-y,2)^2 | ||
| − | + | ||
reg - regularisation signal norm(D*x,2)^2 | reg - regularisation signal norm(D*x,2)^2 | ||
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==Notes== | ==Notes== | ||
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For best numerical performance, scale K to have approximately unit 2-norm, and y to have approximately unit 1-norm. | For best numerical performance, scale K to have approximately unit 2-norm, and y to have approximately unit 1-norm. | ||
==See also== | ==See also== | ||
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[[Import,_export,_and_visualisation#Miscellaneous_data_processing|Miscellaneous data processing]] | [[Import,_export,_and_visualisation#Miscellaneous_data_processing|Miscellaneous data processing]] | ||
Revision as of 15:50, 5 April 2026
Analytical Tikhonov regularised solution to K*x=y without any constraints (indeterminate output).
Syntax
[x,err,reg]=tikhoind(K,D,y,lam)
Arguments
K - kernel matrix, may be complex, may be non-square
D - regularisation matrix, leave empty to use finite
difference second derivative matrix
y - a column vector, may be complex
lam - Tikhonov regularisation parameter
Outputs
x - a real vector, a minimum of
norm(K*x-y,2)^2+lambda*norm(D*x,2)^2
err - error signal norm(K*x-y,2)^2
reg - regularisation signal norm(D*x,2)^2
Notes
For best numerical performance, scale K to have approximately unit 2-norm, and y to have approximately unit 1-norm.
See also
Version 2.9, authors: Ilya Kuprov
