We introduce some iterative methods for solving the linear system $\boldsymbol{Ax}=\boldsymbol{b}$ in this chapter. Why do we need iterative methods? Reduce the cost ...

We cover three strategies of Classical Iterations: Jacobi, Gauss-Seidel and SOR(Successive Over-Relaxation) method. Task: Solve linear system $\boldsymbol{Ax}=\boldsymbol{b}$. Let us discuss the ...

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where ...

Abstract: Resilience is an important research topic in HPC. As computer clusters go to extreme scales, work in this area is necessary to keep these machines reliable. In this work, we introduce a ...

Abstract: Iterative linear solvers are a crucial kernel in many numerical analysis problems. The performance and energy efficiency of iterative solvers based on traditional architectures are severely ...

This is a preview. Log in through your library . Abstract We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic ...

Many linear inverse problems can be formulated as convex optimization problems. These can be solved using iterative schemes that involve gradients and proximal operators of the functionals.