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Full-Text Articles in Physical Sciences and Mathematics
Pólya’S Theorem With Zeros, Mari Castle, Victoria Powers, Bruce Reznick
Pólya’S Theorem With Zeros, Mari Castle, Victoria Powers, Bruce Reznick
Faculty and Research Publications
Let be the real polynomial ring in variables. Pólya’s Theorem says that if a homogeneous polynomial is positive on the standard -simplex , then for sufficiently large all the coefficients of are positive. We give a complete characterization of forms, possibly with zeros on , for which there exists so that all coefficients of have only nonnegative coefficients, along with a bound on the needed.
The Minimum-Norm Least-Squares Solution Of A Linear System And Symmetric Rank-One Updates, Xuzhou Chen, Jun Ji
The Minimum-Norm Least-Squares Solution Of A Linear System And Symmetric Rank-One Updates, Xuzhou Chen, Jun Ji
Faculty and Research Publications
In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.
Sharp Asymptotics Of The Lp Approximation Error For Interpolation On Block Partitions, Yuliya Babenko, Tatyana Leskevich, Jean-Marie Mirebeau
Sharp Asymptotics Of The Lp Approximation Error For Interpolation On Block Partitions, Yuliya Babenko, Tatyana Leskevich, Jean-Marie Mirebeau
Faculty and Research Publications
Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed and no exact formula for the optimal error of approximation can be given. Therefore, the next natural question would be to study the asymptotic behavior of the error and construct asymptotically optimal sequences of partitions. In this paper we provide sharp asymptotic …
Which Chessboards Have A Closed Knight's Tour Within The Rectangular Prism?, Joseph Demaio, Mathew Bindia
Which Chessboards Have A Closed Knight's Tour Within The Rectangular Prism?, Joseph Demaio, Mathew Bindia
Faculty and Research Publications
A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the m x n rectangular chessboards that admit a closed knight's tour. In honor of the upcoming twentieth anniversary of the publication of Schwenk's paper, this article extends his result by classifying the i x j x k rectangular prisms that admit a closed knight's tour.