Mashetti Ravibabu

Mashetti Ravibabu

The SOAR method for computing an orthonormal basis of a second-order Krylov subspace can be numerically unstable (see Lu et al. (2016)). In the Two-level orthogonal Arnoldi(TOAR) procedure, an alternative to SOAR, the problem of instability had circumvented. A stability analysis of the second-order Krylov subspace's orthonormal basis in TOAR with respect to the coefficient matrices of a quadratic problem remain open; see Lu et al. (2016). This paper proposes the Improved-TOAR method(I-TOAR) and solves the said open problem for I-TOAR.

Mashetti Ravibabu

This paper derives a necessary and sufficient condition for the coincidence of Harmonic residual vectors and the residual vector in GMRES. The properties of the harmonic Ritz values at the stagnation of GMRES were described in the Proposition-4.2 of [1]. Necessary and sufficient conditions basing on Harmonic Ritz vectors for the stagnation have derived in this paper.

Mashetti Ravibabu

This paper derives bounds for the ratio of residual norms in the refined and Rayleigh- Ritz projection methods. To do this, it uses the Least squares and line search projection method proposed in [6]. The bound derived in this paper is less costly to compute. Further, it is practically useful to assess the superiority of the refined and the Rayleigh-Ritz projection methods one over the other.

Mashetti Ravibabu

This paper has proposed the GMRES that augments Krylov subspaces with a set of approximate right singular vectors. The proposed method suppresses the error norms of a linear system of equations. Numerical experiments comparing the proposed method with the Standard GMRES and GMRES with eigenvectors methods[3] have been reported for benchmark matrices.

Mashetti Ravibabu

Each iteration in Jacobi-Davidson method for solving large sparse eigenvalue problems involves two phases, called subspace expansion and eigen pair extraction. The subspace expansion phase involves solving a correction equation. We propose a modification to this by introducing a related correction equation, motivated by the least squares. We call the proposed method as the Modified Jacobi-Davidson Method. When the subspace expansion is ignored as in the Simplified Jacobi- Davidson Method, the modified method is called as Modified Simplified Jacobi-Davidson Method. We analyze the convergence properties of the proposed method for Symmetric matrices. Numerical experiments have been carried out to check whether the method is computationally viable or not.