The exact analysis of sparse rectangular linear systems

Development of the package documented in this paper was motivated by the study of multivariate spline spaces. A multivariate spline is a smooth (i. e., one or more times differentiable) piecewise polynomial function defined on a partition of a domain in 2 (or higher) dimensional space. Such splines have a large potential for applications, e.g., in representing data, multivariate interpolation and approximation, and computer-aided geometric design. HOWever, the structure of multivariate spline spaces is extremely complicated, only poorly understood, and currently under intense scrutiny. For an introduction to the literature on splines see Chui [9] and Lyche and Schumaker [22] and the references therein. A standard way of’ representing a multivariate spline space is as a subspace of a larger (but more simply structured) space. The sub space is described by a system of linear equations which force the smoothness of the subspace. Such systems are typically homogeneous, very large, sparse, rectangular and rank-deficient. The spline space in question is isomorphic to the

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