Cache Efficient Implementation for Block Matrix Operations

Efficiently manipulating and operating on block matrices can be beneficial in many applications, among others those involving iteratively solving nonlinear systems. These types of problems consist of repeatedly assembling and solving sparse linear systems. In the case of very large systems, without a careful manipulation of the corresponding matrices, solving can become very time consuming.

This paper proposes a memory storage scheme convenient for both, numeric and structural matrix modification and, at the same time, allowing efficient arithmetic operation. This scheme was used in the implementation of a simple BLAS-like library. The advantage of the new scheme is demonstrated through exhaustive tests on the popular University of Florida Sparse Matrix Collection. Furthermore, this library was used in solving several nonlinear graph optimization problems.