Generalized rank annihilation method. I: Derivation of eigenvalue problems

Derivation of the generalized rank annihilation method (GRAM)

Introduction The generalized rank annihilation method (GRAM) is a method for curve resolution and calibration that requires only a single calibration sample to obtain the socalled second-order advantage, i.e., it can determine the analyte of interest in the presence of unsuspected interferences [1]. GRAM is only one of many competing methods that can be applied to this particular data set-up. H...

Generalized Rank Annihilation Method . 111 : Practical Implementation

Derivation of Eigenvalue Problems

A projection method for generalized eigenvalue problems

In this paper, we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane. The proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration. The projection produces a small pencil with Hankel matrices.

The Jacobi-Davidson Method for Eigenvalue and Generalized Eigenvalue Problems

We consider variants of Davidson's method for the iterative computation of one or more eigenvalues and their corresponding eigenvectors of an n n matrix A. The original Davidson method 3], for real normal matrices A, may be viewed as an accelerated Gauss-Jacobi method, and the success of the method seems to depend quite heavily on diagonal dominance of A 3, 4, 17]. In the hope to enlarge the sc...