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Alexandre Eremenko
Alexandre Eremenko
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This question has been studied in two papers of Peter Yuditskii and myself: Zbl 1241.41005 (arXiv:1008.3765) and Zbl 1168.30020 (arXiv:math/0604324), where we determined the polynomial of best approximation to sgn(x), and the asymptotics of the error term. For the general case, take a linear combination of shifts sgn(x-a_j). There is no "Gibbs phenomenon" in this situation.

This question has been studied in two papers of Peter Yuditskii and myself: Zbl 1241.41005 (arXiv:1008.3765) and Zbl 1168.30020 (arXiv:math/0604324), where we determined the polynomial of best approximation to sgn(x), and the asymptotics of the error term. For the general case, take a linear combination of shifts sgn(x-a_j).

This question has been studied in two papers of Peter Yuditskii and myself: Zbl 1241.41005 (arXiv:1008.3765) and Zbl 1168.30020 (arXiv:math/0604324), where we determined the polynomial of best approximation to sgn(x), and the asymptotics of the error term. For the general case, take a linear combination of shifts sgn(x-a_j). There is no "Gibbs phenomenon" in this situation.

Source Link
Alexandre Eremenko
Alexandre Eremenko
  • 91.8k
  • 9
  • 259
  • 429

This question has been studied in two papers of Peter Yuditskii and myself: Zbl 1241.41005 (arXiv:1008.3765) and Zbl 1168.30020 (arXiv:math/0604324), where we determined the polynomial of best approximation to sgn(x), and the asymptotics of the error term. For the general case, take a linear combination of shifts sgn(x-a_j).