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- W2034558750 abstract "Let S ={ s 1 , s 2 ,..., s n } be a set of sites in E d , where every site s i has a positive real weight ω i . This paper gives algorithms to find weighted orthogonal L ∞ and L 1 approximating hyperplanes for S . The algorithm for the weighted orthogonal L 1 approximation is shown to require O( n d ) worst-case time and O( n ) space for d ≥ 2. The algorithm for the weighted orthogonal L ∞ approximation is shown to require O( n log n ) worst-case time and O( n ) space for d = 2, and O( n ⌊ dl 2 + 1⌋ ) worst-case time and O( n ⌊( d +1)/2⌋ ) space for d > 2. In the latter case, the expected time complexity may be reduced to O( n ⌊( d +1)/2⌋ ). The L ∞ approximation algorithm can be modified to solve the problem of finding the width of a set of n points in E d , and the problem of finding a stabbing hyperplane for a set of n hyperspheres in E d with varying radii. The time and space complexities of the width and stabbing algorithms are seen to be the same as those of the L ∞ approximation algorithm." @default.
- W2034558750 created "2016-06-24" @default.
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- W2034558750 date "1993-06-01" @default.
- W2034558750 modified "2023-09-25" @default.
- W2034558750 title "Orthogonal weighted linear L1 and L∞ approximation and applications" @default.
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- W2034558750 doi "https://doi.org/10.1016/0166-218x(93)90113-3" @default.
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