On the p-norm condition number of the multivariate triangular Bernstein basis
نویسندگان
چکیده
منابع مشابه
On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis
We give an upper bound for the L condition number of the triangular Bernstein basis for polynomials of total degree at most n in s variables. The upper bound grows like (s + 1) when n tends to infinity. Moreover the upper bound is independent of s for s ≥ n− 1.
متن کاملOn the L1-Condition Number of the Univariate Bernstein Basis
We show that the size of the 1-norm condition number of the univariate Bernstein basis for polynomials of degree n is O(2n/ √ n). This is consistent with known estimates [3], [5] for p = 2 and p = ∞ and leads to asymptotically correct results for the p-norm condition number of the Bernstein basis for any p with 1 ≤ p ≤ ∞.
متن کاملAddendum to ”On the L1-Condition Number of the Univariate Bernstein Basis”
The paper mentioned above is a contribution of the authors to volume 18(2002) of this journal, see [1] . Recently J. Domsta pointed out to us that the proof of Theorem 4.2 in that paper contains an error. The purpose of this note is to present a correct argument for it. §
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15 صفحه اولVerified Bounds for the p-Norm Condition Number
Methods to compute verified error bounds for the p-norm condition number of a matrix are discussed for p ∈ {1, 2,∞} and the Frobenius norm. We consider the cases of a real or complex, point or interval input matrix. In the latter case the condition number of all matrices within the interval matrix are bounded. A special method for extremely ill-conditioned matrices is derived as well. Numerical...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2000
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00383-6