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61.
Hirozumi Fujii 《Proceedings of the American Mathematical Society》1996,124(9):2923-2933
It is well-known that any Laurent polynomial satisfying and is the Alexander polynomial of a knot in . We show that can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.
62.
Z. Ditzian 《Proceedings of the American Mathematical Society》1996,124(6):1773-1781
We show that the -functional
where , is equivalent to the rate of convergence of a certain linear polynomial operator. This operator stems from a Riesz-type summability process of expansion by Legendre polynomials. We use the operator above to obtain a linear polynomial approximation operator with a rate comparable to that of the best polynomial approximation.
63.
Vera V. Kovacevic-Vujcic 《Mathematical Programming》1991,52(1-3):467-479
This paper proposes a procedure for improving the rate of convergence of interior point methods for linear programming. If (x
k
) is the sequence generated by an interior point method, the procedure derives an auxiliary sequence (
). Under the suitable assumptions it is shown that the sequence (
) converges superlinearly faster to the solution than (x
k
). Application of the procedure to the projective and afflne scaling algorithms is discussed and some computational illustration is provided. 相似文献
64.
In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators. 相似文献
65.
66.
《Discrete Mathematics》2023,346(6):113349
The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations. 相似文献
67.
We extend the concept of the difference dimension polynomial of a difference field extension to difference local algebras. The main theorem of the paper establishes the existence and form of the dimension polynomial associated with the localization of a finitely generated well-mixed difference algebra at a prime reflexive difference ideal. 相似文献
68.
69.
Sheldon P. Gordon 《International Journal of Mathematical Education in Science & Technology》2017,48(3):455-473
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials. 相似文献
70.
LAO HUI-XUE 《东北数学》2012,28(2)
Under the assumption of sixth power large sieve mean-value of Dirichlet L-function,we improve Bombieri's theorem in short intervals by virtue of the large sieve method and Heath-Brown's identity. 相似文献