tikhoind.m

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

Note: for best numerical performance, scale K to have approxima-
      tely unit 2-norm, and y to have approximately unit 1-norm.

Note: see tikhonov.m for the positive-constraned solver.

ilya.kuprov@weizmann.ac.il

Notes

For best numerical performance, scale K to have approximately unit 2-norm, and y to have approximately unit 1-norm.

See also

Miscellaneous data processing

Numerical infrasctucture

tikhonov.m

Version 2.9, authors: Ilya Kuprov