Difference between revisions of "Tikhoind.m"
(Created page with "{{DISPLAYTITLE:tikhoind.m}} __NOTOC__ Analytical Tikhonov regularised solution to K*x=y without any constraints (indeterminate output). ==Syntax== [x,err,reg]=tikhoind(...") |
(→See also) |
||
| Line 30: | Line 30: | ||
==See also== | ==See also== | ||
| − | [[Kernel_utilities#Numerical_infrastructure|Numerical | + | [[Import,_export,_and_visualisation#Miscellaneous_data_processing|Miscellaneous data processing]] |
| + | |||
| + | [[Kernel_utilities#Numerical_infrastructure|Numerical infrasctucture]] | ||
| + | |||
| + | [[tikhonov.m]] | ||
''Version 2.9, authors: [[Ilya Kuprov]]'' | ''Version 2.9, authors: [[Ilya Kuprov]]'' | ||
Revision as of 09:44, 4 May 2024
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
