Krylov-subspace methods, such as the multistage Wiener filter and conjugate gradient method, are often used for reduced-dimension adaptive beamforming. These techniques do not, however, allow for steering vector mismatch, which is typically present in many applications of interest, including passive sonar. Here, we discuss recently proposed robust methods that do allow for steering vector misma...

Consider the linear system Ax = b, where A ∈ CN×N is a singular matrix. In the present work we propose a general framework within which Krylov subspace methods for Drazininverse solution of this system can be derived in a convenient way. The Krylov subspace methods known to us to date treat only the cases in which A is hermitian and its index ind(A) is unity necessarily. In the present work A i...

We conduct an experimental study on the behavior of several preconditioned iterative methods to solve nonsymmetric matrices arising from computational ̄uid dynamics (CFD) applications. The preconditioned iterative methods consist of Krylov subspace accelerators and a powerful general purpose multilevel block ILU (BILUM) preconditioner. The BILUM preconditioner and an enhanced version of it are ...

One of the most powerful tools for solving large and sparse systems of linear algebraic equations is a class of iterative methods called Krylov subspace methods. Their significant advantages like low memory requirements and good approximation properties make them very popular, and they are widely used in applications throughout science and engineering. The use of the Krylov subspaces in iterati...

This talk summarizes recent analysis of an alternative approach to the solution of diffusion problems and wave propagation problems in the variable-coefficient case that leads to a new class of numerical methods, called Krylov subspace spectral methods [3]. The basic idea behind these methods, applied to a PDE of the form du/dt + L(x,D)u = 0, is to use Gaussian quadrature in the spectral domain...