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Shift for nonsymmetric generalised eigenvalue problems
In this paper we analyze inexact inverse iteration for the nonsymmetric generalized eigenvalue problem Ax = λMx, where M is symmetric positive definite and the problem is diagonalizable. Our analysis is designed to apply to the...
A low-rank approach to the solution of weak constraint variational data assimilation problems
Weak constraint four-dimensional variational data assimilation is an important method for incorporating data (typically observations) into a model. The linearised system arising within the minimisation process can be formulated...
Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves
We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple...
Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves
We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple...
Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems
Convergence results are provided for inexact inverse subspace iteration applied to the problem of finding the invariant subspace associated with a small number of eigenvalues of a large sparse matrix. These results are...
A low-rank approach to the solution of weak constraint variational data assimilation problems
Weak constraint four-dimensional variational data assimilation is an important method for incorporating data (typically observations) into a model. The linearised system arising within the minimisation process can be formulated...
Inexact inverse iteration for symmetric matrices
In this paper we analyse inexact inverse iteration for the real symmetric eigenvalue problem Av = λv. Our analysis is designed to apply to the case when A is large and sparse and where iterative methods are used to solve the...
Inexact inverse iteration for symmetric matrices
In this paper we analyse inexact inverse iteration for the real symmetric eigenvalue problem Av = λv. Our analysis is designed to apply to the case when A is large and sparse and where iterative methods are used to solve the...
Shift for nonsymmetric generalised eigenvalue problems
In this paper we analyze inexact inverse iteration for the nonsymmetric generalized eigenvalue problem Ax = λMx, where M is symmetric positive definite and the problem is diagonalizable. Our analysis is designed to apply to the...
Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems
Convergence results are provided for inexact inverse subspace iteration applied to the problem of finding the invariant subspace associated with a small number of eigenvalues of a large sparse matrix. These results are...