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Stefan Kohl ♦
Stefan Kohl ♦
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Error Boundsbounds for Approximationapproximation with Dyadic Sumsdyadic sums of Polynomialspolynomials

areAre there any bounds known for approximating a genuine multidimensional polynomial function with a sum one-dimensional polynomials over the independent variables?

In the twodimensional2-dimensional case the expression to be minimized would be: $$\left\| \sum_{i=0}^m\sum_{j=0}^nc_{ij}x^iy^j\ - \left(\sum_{k=0}^{m+n} a_kx^k+b_ky^k\right) \right\|$$

I am mainly interested in the standard cases of the $L_p$ norms (i.e. for $p=\infty,2,1$ in the order of preference), but results related to other error measures are also appreciated.

Error Bounds for Approximation with Dyadic Sums of Polynomials

are there any bounds known for approximating a genuine multidimensional polynomial function with a sum one-dimensional polynomials over the independent variables?

In the twodimensional case the expression to be minimized would be: $$\left\| \sum_{i=0}^m\sum_{j=0}^nc_{ij}x^iy^j\ - \left(\sum_{k=0}^{m+n} a_kx^k+b_ky^k\right) \right\|$$

I am mainly interested in the standard cases of the $L_p$ norms (i.e. for $p=\infty,2,1$ in the order of preference), but results related to other error measures are also appreciated.

Error bounds for approximation with dyadic sums of polynomials

Are there any bounds known for approximating a genuine multidimensional polynomial function with a sum one-dimensional polynomials over the independent variables?

In the 2-dimensional case the expression to be minimized would be: $$\left\| \sum_{i=0}^m\sum_{j=0}^nc_{ij}x^iy^j\ - \left(\sum_{k=0}^{m+n} a_kx^k+b_ky^k\right) \right\|$$

I am mainly interested in the standard cases of the $L_p$ norms (i.e. for $p=\infty,2,1$ in the order of preference), but results related to other error measures are also appreciated.

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Manfred Weis
Manfred Weis
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Error Bounds for Approximation with Dyadic Sums of Polynomials

are there any bounds known for approximating a genuine multidimensional polynomial function with a sum one-dimensional polynomials over the independent variables?

In the twodimensional case the expression to be minimized would be: $$\left\| \sum_{i=0}^m\sum_{j=0}^nc_{ij}x^iy^j\ - \left(\sum_{k=0}^{m+n} a_kx^k+b_ky^k\right) \right\|$$

I am mainly interested in the standard cases of the $L_p$ norms (i.e. for $p=\infty,2,1$ in the order of preference), but results related to other error measures are also appreciated.