Date of Award
5-2025
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
School
Mathematics and Natural Sciences
Committee Chair
James Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Haiyan Tian
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Huiqing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
Committee Member 4
John Harris
Committee Member 4 School
Mathematics and Natural Sciences
Abstract
In this dissertation, we present an iterative method (Preconditioned Nonsymmetric Saddle Point Conjugate Gradient) for simultaneously solving forward ($A{\bf x}={\bf b}$) and adjoint ($A^T{\bf y}={\bf g}$) linear systems. Our approach involves constructing an augmented nonsymmetric saddle point matrix that has a real positive spectrum and developing a conjugate gradient-like iteration for this matrix. We investigate the use of Schur Complement preconditioners with block-diagonal factorization computed by an incomplete QR factorization of $A$ to speed up the convergence of our method and compare the results to the preconditioned generalized least squares residual (GLSQR) and quasi-minimal residual (QMR) methods. We develop quadrature rules based on our NspCG method for estimating the generic bilinear form ${\bf u}^Tf(A){\bf v}$ necessary for approximating the scattering amplitude ${\bf g}^TA^{-1}{\bf b}$.
ORCID ID
0009-0008-1736-5678
Copyright
Samson Ayo
Recommended Citation
Ayo, Samson, "Solution of Preconditioned Nonsymmetric Saddle Point Systems through Modified Conjugate Gradient Iteration" (2025). Dissertations. 2348.
https://aquila.usm.edu/dissertations/2348