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Improving Efficiency Of Rational Krylov Subspace Methods, Shengjie Xu

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This thesis studies two classes of numerical linear algebra problems, approximating the product of a function of a matrix with a vector, and solving the linear eigenvalue problem $Av=\lambda Bv$ for a small number of eigenvalues. These problems are solved by rational Krylov subspace methods (RKSM). We present several improvements in two directions: pole selection and applying inexact methods.

In Chapter 3, a flexible extended Krylov subspace method ($\mathcal{F}$-EKSM) is considered for numerical approximation of the action of a matrix function $f(A)$ to a vector $b$, where the function $f$ is of Markov type. $\mathcal{F}$-EKSM has the same framework as …