Iterative Methods for the Partial Symmetric Eigenproblem

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...

Iterative Methods for Neutron Transport Eigenvalue Problems

We discuss iterative methods for computing criticality in nuclear reactors. In general this requires the solution of a generalised eigenvalue problem for an unsymmetric integro-differential operator in 6 independent variables, modelling transport, scattering and fission, where the dependent variable is the neutron angular flux. In engineering practice this problem is often solved iteratively, u...

Jacobi - Davidson style QR and QZ algorithmsfor the partial reduction of matrix pencilsbyDiederik

The Jacobi-Davidson subspace iteration method ooers possibilities for solving a variety of eigen-problems. In practice one has to apply restarts because of memory limitations, in order to restrict computational overhead, and also if one wants to compute several eigenvalues. In general, restarting has negative eeects on the convergence of subspace methods. We will show how eeective restarts can ...

Iterative Method for Mirror-Symmetric Solution of Matrix Equation AXB + CY D = E

An Arnoldi Method for Nonlinear Symmetric Eigenvalue Problems

where T (λ) ∈ R is a family of symmetric matrices depending on a parameter λ ∈ J , and J ⊂ R is an open interval which may be unbounded. As in the linear case T (λ) = λI −A a parameter λ is called an eigenvalue of T (·) if problem (1) has a nontrivial solution x 6= 0 which is called a corresponding eigenvector. We assume that the matrices T (λ) are large and sparse. For sparse linear eigenvalue...