Additive preconditioning, eigenspaces, and the inverse iteration
نویسندگان
چکیده
منابع مشابه
Additive Preconditioning , Eigenspaces , and the Inverse Iteration ∗
We incorporate our recent preconditioning techniques into the classical inverse power (Rayleigh quotient) iteration for computing matrix eigenvectors. Every loop of this iteration essentially amounts to solving an ill conditioned linear system of equations. Due to our modification we solve a well conditioned linear system instead. We prove that this modification preserves local quadratic conver...
متن کاملTR-2007004: Additive Preconditioning, Eigenspaces, and the Inverse Iteration
Previously we have showed that the computation of vectors in and bases for the null space of a singular matrix can be accelerated based on additive preconditioning and aggregation. Now we incorporate these techniques into the inverse iteration for computing the eigenvectors and eigenspaces of a matrix, which are the null vectors and null spaces of the same matrix shifted by its eigenvalues. Acc...
متن کاملTR-2008006: Additive Preconditioning, Eigenspaces, and the Inverse Iteration
We incorporate our recent preconditioning techniques into the classical inverse power (Rayleigh quotient) iteration for computing matrix eigenvectors. Every loop of this iteration essentially amounts to solving an ill conditioned linear system of equations. Due to our modification we solve a well conditioned linear system instead. We prove that this modification preserves local quadratic conver...
متن کاملPreconditioning CGNE iteration for inverse problems
The conjugate gradient method applied to the normal equations (cgne) is known as one of the most efficient methods for the solution of (non-symmetric) linear equations. By stopping the iteration according to a discrepancy principle, cgne can be turned into a regularization method. We show that cgne can be accelerated by preconditioning in Hilbert scales, derive (optimal) convergence rates with ...
متن کاملOn the Relationships Between Power Iteration, Inverse Iteration and FastICA
In recent years, there has been an increasing interest in developing new algorithms for digital signal processing by applying and generalising existing numerical linear algebra tools. A recent result shows that the FastICA algorithm, a popular state-of-the-art method for linear Independent Component Analysis (ICA), shares a nice interpretation as a Newton type method with the Rayleigh Quotient ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2009
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.07.006