Erismann

Erismann, in the context of numerical linear algebra, often refers to methods or techniques related to sparse matrix direct solvers. Specifically, it is commonly associated with the work of Arnold M. Erismann, a prominent figure in the development and implementation of algorithms for solving large, sparse systems of linear equations. His contributions have been crucial in areas such as power system analysis, circuit simulation, and structural engineering, where sparse matrices arise frequently.

Erismann's research focused on efficient methods for LU decomposition of sparse matrices, which involves factoring the matrix into a lower triangular matrix (L) and an upper triangular matrix (U). Key aspects of his work include:

• Ordering Strategies: The order in which rows and columns are permuted significantly impacts the fill-in (creation of non-zero elements) during LU decomposition of a sparse matrix. Erismann developed and analyzed various ordering algorithms, aiming to minimize fill-in and thus reduce the storage and computational cost. Common strategies include minimum degree ordering and variants thereof.

• Data Structures for Sparse Matrices: Efficient storage and manipulation of sparse matrices are essential for performance. Erismann's work often involved exploring and optimizing data structures suitable for storing and operating on sparse matrices, such as compressed row storage (CRS) and compressed column storage (CCS).

• Software Development: Erismann contributed to the development of software packages and libraries for solving sparse linear systems, making these techniques more accessible to researchers and practitioners.

While "Erismann" is not a specific algorithm or theorem in itself, it serves as an identifier for the body of work related to his contributions in sparse matrix direct solvers, especially the ordering and factorization techniques used to efficiently solve large, sparse linear systems. Referencing "Erismann" often points to the principles and methodologies associated with reducing fill-in during sparse matrix factorization, thereby improving the efficiency of direct solvers.