Carl D. Meyer

Matrix analysis and applied linear algebra

Preface 1. Linear equations 2. Rectangular systems and echelon forms 3. Matrix algebra 4. Vector spaces 5. Norms, inner products, and orthogonality 6. Determinants 7. Eigenvalues and Eigenvectors 8. Perron-Frobenius theory of nonnegative matrices Index.

A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method

A method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix

A Survey of Eigenvector Methods for Web Information Retrieval

A

The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains

is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations. It is proved that in exact arithmetic the preconditioner is well defined if

Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems

A

Comparison of perturbation bounds for the stationary distribution of a Markov chain

is an H-matrix. The results of numerical experiments are presented.

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

Web information retrieval is significantly more challenging than traditional well-controlled, small document collection information retrieval. One main difference between traditional information retrieval and Web information retrieval is the Webs hyperlink structure. This structure has been exploited by several of todays leading Web search engines, particularly Google and Teoma. In this survey paper, we focus on Web information retrieval methods that use eigenvector computations, presenting the three popular methods of HITS, PageRank, and SALSA.

The idea behind Krylov methods

For an m-state homogeneous Markov chain whose one-step transition matrix is T, the group inverse,

The Index and the Drazin Inverse of Block Triangular Matrices

A^#

Generalized Inversion of Modified Matrices

, of the matrix