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Appendix to "Approximation of viscosity solutions of elliptic partial differential equations on minimal grids", by M. Kocan: Approximation to orthogonal bases in\({\Bbb R}^n\) by orthogonal bases with integer coordinates

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In the Appendix it is shown that given\(N>1\) , an orthogonal basis\(\underline{\underline {\varphi_1}},\dots, \underline{\underline{\varphi_n}}\) of\({\Bbb R}^n\) where\(n\ge4\) can be approximated by an orthogonal basis\(\underline{\underline{a_1}},\dots, \underline{\underline{a_n}}\) with integer components such that the angle between\(\underline{\underline{\varphi_i}}\) and \(\underline{\underline{a_i}}\) is at most\(1/N\) \((i=1,\dots,n)\) , and\(\underline{\underline {a_1}},\dots, \underline{\underline{a_n}}\) have norms\(\ll N^{2n-4}\) .

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Received 10 January 1995

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Schmidt, W. Appendix to "Approximation of viscosity solutions of elliptic partial differential equations on minimal grids", by M. Kocan: Approximation to orthogonal bases in\({\Bbb R}^n\) by orthogonal bases with integer coordinates . Numer Math 72, 117–122 (1995). https://doi.org/10.1007/s002110050162

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  • DOI: https://doi.org/10.1007/s002110050162

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