Compression approaches for the regularized solutions of linear systems from large-scale inverse problems (Q901334)

The paper studies regularized solutions of large and sparse linear ill-posed problems. In order to make the computation more effective, it is proposed to approximate the matrix-vector product using a smaller and sparser matrix \(M\) constructed based on wavelet transformations. Then it is shown how to compute lower rank approximations of the original matrix by a randomized algorithm based on the matrix \(M\). Error bounds for the obtained regularized solutions are derived. A block matrix implementation for particular applications is also mentioned.