Talk:Tikhonov regularization

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Contents 1 Generalized Tikhonov 2 Generalized Tikhonov - correction 3 Least Squares Solution 4 Textbooks? 5 General Form

[edit] Generalized Tikhonov

The formula

x₀+ (A^TP A + Q)^-1A^TP(b- Ax₀)

is from Tarantola, eg (1.93) page 70. There are several other equivalent formulas.

[edit] Generalized Tikhonov - correction

It should be α²Q instead of just Q.

[edit] Least Squares Solution

"For α = 0 this reduces to the least squares solution of an overdetermined problem (m > n)."

This isn't correct. (A^TA)^-1 won't exist unless A has full column rank, and (m>n) does not imply that A has full column rank. The sentence should read "For α = 0 this reduces to the least squares solution provided that (A^TA)^-1 exists."

[edit] Textbooks?

I take it that Tikhonov regularization is not discussed in text books yet? If it is, I would love a reference. 17:50, 16 October 2006 (UTC)

[edit] General Form

Why not mentioning the general form incorporating an arbitrary smoothing operator (i.e. derivation operators) instead of just the identity matrix in special? Ref.: Hansen, P. C.: Rank-Deficient and Discrete Ill-posed Problems