I am solving $Ax=b$ for a huge sparse positive definite matrix $A$ using the conjugate gradient (CG) method. It is possible to compute the determinant of $A$ using the information produced during the ...
What is a good way to check if the any numerical error is occured in conjugate gradient algorithm. Additionally why is it not suggested to check error by checking A-orthogonality of search direction ...
CG may be used to estimate the extremal eigenvalues of a SPD matrix (by computing eigenvalues of tridiagonal matrix associated with the Lanczos algorithm). After a few iterations the largest ...
Is a checkerboard block decomposition of a matrix useful when solving a linear system with a parallel conjugate gradient method?
According to these lecture notes, a checkerboard block decomposition should exhibit better scalability when applied to parallel matrix-vector multiplication (presumably because of greater cache hit ...
I know that a conjugate gradient method is guaranteed to converge to the solution of a linear system if the matrix is positive definite. I'm working with a family of matrices that have the following ...
What is the principle behind the convergence of Krylov subspace methods for solving linear systems of equations?
As I understand it, there are two major categories of iterative methods for solving linear systems of equations: Stationary Methods (Jacobi, Gauss-Seidel, SOR, Multigrid) Krylov Subspace methods ...
I am looking for a reference - paper, book, discussion, anything that has a mathematical proof for stability of the conjugate gradient method in floating point arithmetic. Something similar for ...