# A Golub–Kahan-Type Reduction Method for Matrix Pairs

@article{Hochstenbach2015AGR, title={A Golub–Kahan-Type Reduction Method for Matrix Pairs}, author={Michiel E. Hochstenbach and Lothar Reichel and Xuebo Yu}, journal={Journal of Scientific Computing}, year={2015}, volume={65}, pages={767-789} }

We describe a novel method for reducing a pair of large matrices $$\{A,B\}$${A,B} to a pair of small matrices $$\{H,K\}$${H,K}. The method is an extension of Golub–Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large linear discrete ill-posed problems are described. In these problems the matrix A represents a discretization of a compact integral operator and B is a regularization matrix.

## 16 Citations

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