GSVDGeneralized Singular Value Decomposition
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To obtain an expression of G([lambda]) easy to handle, one considers the GSVD of the matrix pair (A, L), defined by (1.
m[greater than or equal to]1], we assume that the GSVD decomposition of the matrix pair ([[bar.
This value of [mu] is the solution of a nonlinear equation, which can be solved conveniently by using the GSVD of the matrix pair {[H.
We compare with results obtained by using decompositions determined the GSVD and by [20, Algorithm 2.
We also solve the Tikhonov minimization problem of this example with the aid of the GSVD in the following manner.
An approximate solution is also computed by using the GSVD of the matrix pair {A, [L.
black dash-dotted curve) and the GSVD solution (blue solid curve).
This relative error is smaller than the relative error of the GSVD solution.
Reichel, Rescaling the GSVD with application to ill-posed problems, Numer.