Abstract
The conditioning of spline collocation matrices is considered in the case of a boundary value problem for an mth order equation. For bases with continuity built in (which corresponds to most current implementations of splines for solving ODEs), the collocation matrix A is related to the corresponding multiple shooting matrix for a first order system. This gives the explicit form for $A^{ - 1} $ as a discrete Green function. We briefly discuss the implications for mesh selection and how our results relate to previous ones for finite differences.
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