منابع مشابه
On the generation of Krylov subspace bases
Many problems in scientific computing involving a large sparse matrix A are solved by Krylov subspace methods. This includes methods for the solution of large linear systems of equations with A, for the computation of a few eigenvalues and associated eigenvectors of A, and for the approximation of nonlinear matrix functions of A. When the matrix A is non-Hermitian, the Arnoldi process commonly ...
متن کاملOn Optimal Short Recurrences for Generating Orthogonal Krylov Subspace Bases
In this talk I will discuss necessary and sufficient conditions on a nonsingular matrix A, such that for any initial vector r0, an orthogonal basis of the Krylov subspaces Kn(A, r0) is generated by a short recurrence. Orthogonality here is meant with respect to some unspecified positive definite inner product. This question is closely related to the question of existence of optimal Krylov subsp...
متن کاملThe effect of non-optimal bases on the convergence of Krylov subspace methods
There are many examples where non-orthogonality of a basis for Krylov subspace methods arises naturally. These methods usually require less storage or computational effort per iteration than methods using an orthonormal basis (optimal methods), but the convergence may be delayed. Truncated Krylov subspace methods and other examples of non-optimal methods have been shown to converge in many situ...
متن کاملKrylov subspace iteration
In the simulation of continuous events, such as the ow of a uid through a pipe, or the ow of air around an aircraft, one usually imposes a grid over the area of interest and one restricts oneself to the computation of relevant parameters, for instance the pressure or the velocity of the ow or the temperature, in the gridpoints. Physical laws lead to approximate relations between these parameter...
متن کاملKrylov subspace estimation
Computing the linear least-squares estimate of a high-dimensional random quantity given noisy data requires solving a large system of linear equations. In many situations, one can solve this system e ciently using a Krylov subspace method, such as the conjugate gradient (CG) algorithm. Computing the estimation error variances is a more intricate task. It is di cult because the error variances a...
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ژورنال
عنوان ژورنال: Applied Numerical Mathematics
سال: 2012
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2010.12.009