A number of applications in science and industry require decompositions of large-scale matrices and tensors. Those include linear and nonlinear eigenvalue problems, singular value problems, and structured matrix recovery from incomplete data. Often a small-scale information is sufficient, such as only a few eigenvalues close to a target value, or only a low-rank approximation to the matrix. These problems can be tackled efficiently by iterative methods, such as the inverse iteration, Krylov and alternating gradient descent methods. The image shows the pseudospectrum of an example matrix.

Sergey Dolgov Silvia Gazzola