Stanford University Linear Algebra in Python Problem Paper Please provide as much details as possible. Need to be correct also. It should be both code and

Stanford University Linear Algebra in Python Problem Paper Please provide as much details as possible. Need to be correct also. It should be both code and graph and comments. Thanks! Problem 2:
Using Julia, we illustrate some of the properties of calculations using finite-precision, as they are done
on a computer. Consider the following two polynomials defined in Julia:
P = x-> ( X.18 – 40*x. 17 + 700*x.^6 – 7000*x. 15 + 43750*X.14
175000*x.^3 + 437500*x.^2 – 625000*x + 390625)
pe = x -> ( (x.-5).^8 )
1. 2 points. How are these polynomials related?
2. 5 points. In Julia, define x = 4:01:6. Plot p(x), pe(x). Plot
abs. ((P(x) – pe(x))./P(x))
using a logarithmic scale on the y-axis (semilogy). Comment on your observations.
3. 5 points. Provide a method to estimate the magnitude of the roundoff errors in a simple way for
this problem.
Plotting in Julia (kernel v1.0):
First
, install the Plots package (note: you may skip this step if using
JuliaBox). In Julia, type] to
enter the package management mode (see course reader for more examples and explanations). Then:
(v1.0) pkg> update
(v1.0) pkg> add plots
(v1.0) pkg> add Pyplot
Hit backspace to come back to Julia. exit() to quit Julia.
Then, the plotting commands are, inside a Julia notebook:
using Plots
pyplot()
https://software.intel.com/blogs/2014/10/03/fxis-documentation improvements-is-the-intel-Ct-and-18-32-architecturex-xoftware
httpx://randomwell.wordpress.com/2014/10/09/Intel-anderestimatex-error-bunda-by-1-3-quintallic
2
X = 4:.01:6
plot(X, 1e-20 + abs. ((P(x) – pe(x)) ./ p(x)), yscale : log10,
ylims=(1e-8, 10), label=”Error”)
yaxis! (“Error”)
xaxis! (“x”)

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