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**1 - 2**of**2**### General Terms: Algorithms

"... When working with empirical polynomials, it is important not to introduce unnecessary changes of basis, because that can destabilize fundamental algorithms such as evaluation and rootfinding: for more details, see e.g. [3, 4]. Moreover, in ..."

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When working with empirical polynomials, it is important not to introduce unnecessary changes of basis, because that can destabilize fundamental algorithms such as evaluation and rootfinding: for more details, see e.g. [3, 4]. Moreover, in

### The Nearest Polynomial of Lower Degree

"... Suppose one is working with the polynomial p(x) = −0.99B3 0(x)−1.03B3 1(x)− 0.33B3 2(x) + B3 3(x) expressed in terms of degree 3 Bernstein polynomials and suppose one has reason to believe that p(x) is really of degree 2. Applying the degree-reducing procedure [6] one gets −0.99B2 0(x) − 1.05B2 1( ..."

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Suppose one is working with the polynomial p(x) = −0.99B3 0(x)−1.03B3 1(x)− 0.33B3 2(x) + B3 3(x) expressed in terms of degree 3 Bernstein polynomials and suppose one has reason to believe that p(x) is really of degree 2. Applying the degree-reducing procedure [6] one gets −0.99B2 0(x) − 1.05B2 1(x) + B2 2(x). But