Abstract
Efficient application of iterative methods on large-scale problems brings up many challenges. In this contribution, we focus on computational aspects of discrete inverse problems arising in volume reconstruction in Single particle analysis.
Such problems represent an extremely large-scale well-structured approximation problem Ax~b. We explore the structure and sparsity of the matrix A and discuss how these properties depend on various discretization approaches.
Further, we focus on the implementation of matrix-vector products, a vital part of iterative methods. We describe computation of parallel matrix-vector products with the matrix A on GPUs and explain why sparsity is crucial for parallel multiplication with the transpose of the matrix A.