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The long-standing problem of minimal projections is addressed from acomputational point of view. Techniques to determine bounds on the projectionconstants of univariate polynomial spaces are presented. The upper bound,produced by a linear program, and the lower bound, produced by a semidefiniteprogram exploiting the method of moments, are often close enough to deduce theprojection constant with reasonable accuracy. The implementation of theseprograms makes it possible to find the projection constant of severalthree-dimensional spaces with five digits of accuracy, as well as theprojection constants of the spaces of cubic, quartic, and quintic polynomialswith four digits of accuracy. Beliefs about uniqueness and shape-preservationof minimal projections are contested along the way.

Determining Projection Constants of Univariate Polynomial Spaces