CMP润滑方程的Chebyshev加速超松弛法求解

化学机械抛光（chemicalmechanicalpolishing，CMP）是一项融合了化学分解和机械力学的工艺技术，其中包含了流体动力润滑的作用．文中通过分析流场效应，建立了Sum在化学机械抛光实验基础上获得的润滑（Reynolds）方程，利用Chebyshev加速超松弛技术对润滑方程进行求解，得到了新的抛光液压力分布模型，给出了一些新的载荷及转矩在不同参数下的变化情况．

Modified Chebyshev algorithm: some applications

Two applications of the modified Chebyshev algorithm are considered. The first application deals with the generation of orthogonal polynomials associated with a weight function having singularities on or near the end points of the interval of orthogonality. The other application involves the generation of real Szego polynomials.

A CHEBYSHEV-TYPE QUADRATURE RULE WITH SOME INTERESTING PROPERTIES

We give here an n-point Chebyshev-type rule of algebraic degree of precision n - 1, but having nodes that can be given explicitly. This quadrature rule also turns out to be one with an ''almost'' highest algebraic degree of precision.

Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Il teorema di Chebyshev

Dopo aver introdotto alcune nozioni della teoria della probabilità, ho esposto il teorema di Chebyshev ed alcuni teoremi ad esso collegati. Ho infine analizzato un'applicazione legata alle strategie d'investimento.

Orthogonality relations for Chebyshev polynomials,

"C00-1469-0154."

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"

Spectral approximations to the fractional integral and derivative

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.