An Algorithm for Best Approximating Algebraic Polynomials in L ^p Over a Simplex

Abstract

The set of all algebraic polynomials of of degree m over R ^d is denoted by ∏ _m . For the standard simplex in R ^d,we use the letter Q i.e.:

$$Q=\left\{ \left( {{x}_{1}},\ldots ,{{x}_{d}} \right)\in {{R}^{d}}:{{x}_{1}}+\cdots +{{x}_{d}}\le 1,{{x}_{1}}\ge 0,\ldots ,{{x}_{d}}\ge 0 \right\}$$

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