Abstract
We consider the minimum norm interpolation problem in the [Formula: see text] space, aiming at constructing a sparse interpolation solution. The original problem is reformulated in the pre-dual space, thereby inducing a norm in a related finite-dimensional Euclidean space. The dual problem is then transformed into a linear programming problem, which can be solved by existing methods. With that done, the original interpolation problem is reduced by solving an elementary finite-dimensional linear algebra equation. A specific example is presented to illustrate the proposed method, in which a sparse solution in the [Formula: see text] space is compared to the dense solution in the [Formula: see text] space. This example shows that a solution of the minimum norm interpolation problem in the [Formula: see text] space is indeed sparse, while that of the minimum norm interpolation problem in the [Formula: see text] space is not.
Published Version
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