On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs

11/10/2021
by   Candan Güdücü, et al.
0

We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An important feature of the linear algebraic systems is that the (non-Hermitian) system matrix has a positive definite or semidefinite Hermitian part. In the positive definite case we can solve the linear algebraic systems iteratively by Krylov subspace methods based on efficient three-term recurrences. We illustrate the performance of these iterative methods on several examples. The semidefinite case can be challenging and requires additional techniques to deal with "singular part", while the "positive definite part" can still be treated with the three-term recurrence methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/30/2020

Numerical Method for a Class of Algebraic Riccati Equations

We study an iteration approach to solve the coupled algebraic Riccati eq...
research
07/19/2021

A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations

Solving the normal equations corresponding to large sparse linear least-...
research
04/19/2017

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on ...
research
01/17/2023

A nested divide-and-conquer method for tensor Sylvester equations with positive definite hierarchically semiseparable coefficients

Linear systems with a tensor product structure arise naturally when cons...
research
05/29/2020

Arnoldi algorithms with structured orthogonalization

We study a stability preserved Arnoldi algorithm for matrix exponential ...
research
11/03/2021

Physarum Inspired Dynamics to Solve Semi-Definite Programs

Physarum Polycephalum is a Slime mold that can solve the shortest path p...

Please sign up or login with your details

Forgot password? Click here to reset