The use of partial least squares (PLS) for handling collinearities among the independent variables X in multiple regression is discussed. Consecutive estimates (rank 1, 2,...) are obtained using theâ€¦ (More)

The Rational Krylov algorithm computes eigenvalues and eigenvectors of a regular not necessarily symmetric matrix pencil. It is a generalization of the shifted and inverted Arnoldi algorithm, whereâ€¦ (More)

An algorithm for the computation of the Jordan normal form of a complex square matrix is given. The definition of the Jordan normal form is modified in order to be applicable when working inâ€¦ (More)

A new algorithm for information retrieval is described. It is a vector space method with automatic query expansion. The original user query is projected onto a Krylov subspace generated by the queryâ€¦ (More)

A numerical algorithm for following a path of solutions to a nonlinear eigenvalue problem is described. It is an Euler-Newton continuation method, where the linear systems are solved with an Arnoldiâ€¦ (More)

A band Lanczos algorithm for the iterative computation of eigenvalues and eigenvectors of a large sparse symmetric matrix is described and tested on numerical examples. It starts with a p dimensionalâ€¦ (More)

A new algorithm is developed which computes a specified number of eigenvalues in any part of the spectrum of a generalized symmetric matrix eigenvalue problem. It uses a linear system routineâ€¦ (More)

A rational Krylov algorithm for eigenvalue computation and model order reduction is described. It is shown how to implement it as a modified shift-and-invert spectral transformation Arnoldiâ€¦ (More)

We present two generalisations of the Krylov subspace method, Arnoldi for the purpose of applying them to nite dimensional eigenvalue problems nonlinear in the eigenvalue parameter. The rst method isâ€¦ (More)