# MCS 477 Alabama A&M Numerical Analysis Using Matlab Script Exam Practice

Description

Problem 1: Use the Cholesky factorization to determine whether the matrix A below
is symmetric positive definite

1 -1 -1
-1 2 1
-1 1 2

. Problem 2: Use your preferred numerical differentiation formula to estimate I
0
(1.2)
given values for I(t)
I(1.0) = 8.2277, I(1.1) = 7.2428, I(1.2) = 5.9908, I(1.3) = 4.5260, I(1.4) = 2.9122.
Compare your answer with the exact derivative of I(t) = 10e
−t/10 sin(2t). Problem 3: Let f(x) = x
x
. Consider the interpolating polynomial with interpolation
nodes x0 = 1, x1 = 1.25, and x2 = 1.5. Give a bound on the error in approximating
f(x) with the interpolating polynomial. Problem 4: Use the composite midpoint rule with m = 10 to approximate the
integrals
(a)
Z π/6
−π/6
cos(x)dx (b)
Z 3
2
1
5 − x
dx (c)
Z 2
0
xe−x
dx.
Problem 5: Repeat Problem 4 with a Matlab script

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Tags:
Interpolating Polynomial

Midpoint Rule

Numerical differentiation formula

Interpolation nodes

Cholesky factorization

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