TABLE OF CONTENTS Since the linear operator plays a crucial role in mathematics, it is not surprising that its finite dimensional form, namely, the matrix, is used throughout all fields of scientific and engineering computing. Some examples are the Jacobian, the Hessian, the stiffness matrix, five-point stencil matrix, seven-point stencil matrix, and so on. One needs to solve a square matrix equation, solve a rectangular matrix equation, find the given values of a matrix, obtain the singular value decomposition of a matrix, transform a matrix by certain operations, and so on. Naturally, there are many software products that support a number of linear algebra computations.
In the field of software for dense computational linear algebra, the scientific community has agreed on the applicability of a set of kernels call BLAS, which stands for Basic Linear Algebra Subprograms.
Since the early days of computational linear algebra, software developers had found it natural and convenient to implement certain low level operations as separate subprograms. Hence, much is to be gained if the community can agree on a set of such operations and a software interface to such operations. Such a proposal was made in [57]. The motivations stated there include the following:
It can serve as a conceptual aid in both the design and coding stages of a programming effort.
It improves the self-documenting quality of code to identify an operation such as the dot product [or other often encountered low level operations in linear algebra] by...
