Abstract
In several applications in science and engineering, different types of matrix problems emerge from the discretization of partial differential equations.
This thesis is devoted to the development of new algorithms to solve this
kind of problems. In particular, when the matrices involved are sparse and
nonsymmetric. The new algorithms are based on the Induced Dimension Reduction method [IDR(s)].
IDR(s) is a Krylov subspace method originally proposed in 2008 to solve systems of linear equations. IDR(s) has received considerable attention due to its stable and fast convergence. It is, therefore, natural to ask if it is possible to extend IDR(s) to solve other matrix problems, and if so, to compare those extensions with other wellestablished methods. This work aims to answer these questions.
The main matrix problems considered in this dissertation are: the standard
eigenvalue problem, the quadratic eigenvalue problem, the solution of systems of linear equations, the solution of sequences of systems of linear equations, and linear matrix equations. We focus on examples that arise from the discretization of partial differential equations.
This thesis is devoted to the development of new algorithms to solve this
kind of problems. In particular, when the matrices involved are sparse and
nonsymmetric. The new algorithms are based on the Induced Dimension Reduction method [IDR(s)].
IDR(s) is a Krylov subspace method originally proposed in 2008 to solve systems of linear equations. IDR(s) has received considerable attention due to its stable and fast convergence. It is, therefore, natural to ask if it is possible to extend IDR(s) to solve other matrix problems, and if so, to compare those extensions with other wellestablished methods. This work aims to answer these questions.
The main matrix problems considered in this dissertation are: the standard
eigenvalue problem, the quadratic eigenvalue problem, the solution of systems of linear equations, the solution of sequences of systems of linear equations, and linear matrix equations. We focus on examples that arise from the discretization of partial differential equations.
Original language  English 

Awarding Institution 

Supervisors/Advisors 

Award date  16 Mar 2018 
Print ISBNs  9789463660198 
DOIs  
Publication status  Published  2018 
Keywords
 Krylov subspace methods
 Induced Dimension Reduction
 system of linear equations
 eigenvalues/eigenvectors approximation
 solution of matrix linear problems