Computing the generalized singular value decomposition
SIAM Journal on Scientific Computing
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
A new Tikhonov regularization method
Numerical Algorithms
Inverse problems for regularization matrices
Numerical Algorithms
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The generalized singular value decomposition (GSVD) often is used to solve Tikhonov regularization problems with a regularization matrix without exploitable structure. This paper describes how the standard methods for the computation of the GSVD of a matrix pair can be simplified in the context of Tikhonov regularization. Also, other regularization methods, including truncated GSVD, are considered. We compare the computational efforts required by the simplified GSVD method and the A-weighted generalized inverse introduced by Elden.