Model reduction methods based on Krylov subspaces

Iterative Methods Based on Krylov Subspaces

with a symmetric and positive definite operator A defined on a Hilbert space V with dimV = N and its preconditioned version PCG. We derive the CG from the projection in A-inner product point of view. We shall use (·, ·) for the standard inner product and (·, ·)A for the inner product introduced by the SPD operator A. When we say ‘orthogonal’ vectors, we refer to the default (·, ·) inner product...

Interpolation-based Parametric Model Reduction using Krylov Subspaces

Projection-Based Model Reduction for Time-Varying Descriptor Systems Using Recycled Krylov Subspaces

We will present a projection approach for model reduction of linear time-varying descriptor systems based on earlier ideas in the work of Philips and others. The idea behind the proposed procedure is based on a multipoint rational approximation of the monodromy matrix of the corresponding differential-algebraic equation. This is realized by orthogonal projection onto a rational Krylov subspace....

mortality forecasting based on lee-carter model

over the past decades a number of approaches have been applied for forecasting mortality. in 1992, a new method for long-run forecast of the level and age pattern of mortality was published by lee and carter. this method was welcomed by many authors so it was extended through a wider class of generalized, parametric and nonlinear model. this model represents one of the most influential recent d...

Reduction of Second Order Systems Using Second Order Krylov Subspaces

By introducing the second order Krylov subspace, a method for the reduction of second order systems is proposed leading to a reduced system of the same structure. This generalization of Krylov subspace involves two matrices and some starting vectors and the reduced order model is found by applying a projection directly to the second order model without any conversion to state space. A numerical...