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代写CEE 598UQ-Assignment 6帮做R编程作业、R作业调试、代写R编程

CEE 598UQ Spring 2020: HW Assignment 6
Due on 5/3/2020 11pm
Instructor: Hadi Meidani ()
Note: For all the problems, email your code(s) and solutions to and
by the due date.
Problem 1. (75 points) Consider the following target function
f(x) = f(x1, x2, · · · , x5) = Π5i=1 sin(ixi),
where xi ∈ [0, 1],∀i. We would like to approximate

[0,1]5
f(x)dx using quadrature. Compare the following
multidimensional quadrature rules:
(a) Tensor product using Clenshaw-Curtis (CC) points at levels 1, 2 and 3.
(b) Sparse grid using CC points at levels 1, 2 and 3.
(c) Sparse grid using Gauss-Legendre quadrature points with the number of points in each dimension being
equal to 1, 2 and 3. compare it with one that does so using sparse grid quadratures at levels 1, 3 and 5.
Note: Clenshaw-Curtis points and their weights are given on Slide 15 of Lecture 20.
Problem 2. (75 points) Using the Stochastic Galerkin approach, find a PCE approximation for y given by
ay = bc + d
where a = 3−0.4Ψ1(z1)+0.02Ψ2(z1), b = −5+0.4Ψ1(z2)+0.4Ψ2(z2), c = 3+0.02Ψ1(z3) and d = 11−3Ψ1(z3)
are four random parameters, where {zi} are independent uniform random variables in [0, 1], and {Ψi} are
Legendre polynomials.

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