Direct methods for sparse matrix solution

Matrix-free Sparse Direct Solvers

Existing direct solvers for large linear systems, especially sparse ones, require the matrices to be explicitly available. In practical computations, often only matrix-vector products instead of the matrix are available, which makes iterative methods the only choice. Here, we derive matrix-free sparse direct solvers based on matrixvector products. Two stages are involved. The first stage is to ...

Sparse Direct Methods for Model Simulation

In this paper, diierent strategies to exploit the sparse structure in the solution techniques for macroeconometric models with forward-looking variables are discussed. First, the stacked model is decomposed into recursive submodels without destroying its original block pattern. Next, we concentrate on how to eeciently solve the sparse linear system in the Newton algorithm. In this frame, a mult...

Optimization Methods for Sparse Matrix-Vector Multiplication

Sparse Matrix Ordering Methods for Interior Point

The main cost of solving a linear programming problem using an interior point method is usually the cost of solving a series of sparse, symmetric linear systems of equations, AA T x = b. These systems are typically solved using a sparse direct method. The rst step in such a method is a reordering of the rows and columns of the matrix to reduce ll in the factor and/or reduce the required work. T...

Decomposition Methods for Sparse Matrix Nearness Problems

We discuss three types of sparse matrix nearness problems: given a sparse symmetric matrix, find the matrix with the same sparsity pattern that is closest to it in Frobenius norm and (1) is positive semidefinite, (2) has a positive semidefinite completion, or (3) has a Euclidean distance matrix completion. Several proximal splitting and decomposition algorithms for these problems are presented ...