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A note on zeros of univariate scalar Bernstein polynomials. (English) Zbl 1505.65197

Summary: In [J. Machchhar and G. Elber, Comput. Aided Geom. Des. 43, 16–26 (2016; Zbl 1417.65087)], an algorithm is presented for computing all real roots of univariate scalar Bernstein polynomials by subdividing the polynomial at a known root and then factoring out the root from the polynomial, resulting in a reduction in problem complexity. This short report presents a speed-up over [loc. cit.], by circumventing the need for subdividing the polynomial each time a root is discovered, an \(O(n^2)\) process, where \(n\) is the order of the polynomial. The subdivision step is substituted for by a polynomial division. This alternative also has some drawbacks which are discussed as well.

MSC:

65H04 Numerical computation of roots of polynomial equations

Citations:

Zbl 1417.65087

Software:

IRIT
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Full Text: DOI

References:

[1] Elber, Gershon, IRIT modeling environment, ver. 11 (January 2016)
[2] Farouki, R. T.; Rajan, V. T., Algorithms for polynomials in Bernstein form, Comput. Aided Geom. Des., 5, 1, 1-26 (1988) · Zbl 0648.65007
[3] Machchhar, Jinesh; Elber, Gershon, Revisiting the problem of zeros of univariate scalar Béziers, Geometric Modeling and Processing 2016. Geometric Modeling and Processing 2016, Comput. Aided Geom. Des., 43, 16-26 (2016) · Zbl 1417.65087
[4] Sederberg, Thomas W.; Meyers, Ray J., Loop detection in surface patch intersections, Comput. Aided Geom. Des., 5, 2, 161-171 (1988) · Zbl 0652.65013
[5] Sederberg, Thomas W.; Parry, Scott R., Comparison of three curve intersection algorithms, Comput. Aided Des., 18, 1, 58-63 (1986)
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