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4. Simple stopping criteria for the LSQR method applied to discrete ill-posed problems

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5. Golub–Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems

   https://doi.org/10.1007/s10543-021-00857-0  

   Bai, Xianglan ; Buccini, Alessandro ; Reichel, Lothar ( March 2021 , BIT Numerical Mathematics)

   null (Ed.)

   Abstract Randomized methods can be competitive for the solution of problems with a large matrix of low rank. They also have been applied successfully to the solution of large-scale linear discrete ill-posed problems by Tikhonov regularization (Xiang and Zou in Inverse Probl 29:085008, 2013). This entails the computation of an approximation of a partial singular value decomposition of a large matrix A that is of numerical low rank. The present paper compares a randomized method to a Krylov subspace method based on Golub–Kahan bidiagonalization with respect to accuracy and computing time and discusses characteristics of linear discrete ill-posed problems that make them well suited for solution by a randomized method. 

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