Midterm 2021-exo 3.2

Midterm 2021-exo 3.2

by Marina Rapellini -
Number of replies: 3
Good morning
I wanted to ask how we compute the error in the exercise 3, part 2
Thank you
In reply to Marina Rapellini

Re: Midterm 2021-exo 3.2

by Thomas Weinberger -
Hi Marina,

We have that e_{-1}(t) = f_{-1}(t) - f(t) = f_{0}(t) - f(t)=\frac{1}{2}\psi(t) - f(t), which should best be sketched in order to write down the piecewise defined error function. It seems however that there is a mistake in the solution and all the values in the stated e_{-1}(t) should be multiplied by -1. Maybe this caused your confusion?

Best,
Thomas
In reply to Thomas Weinberger

Re: Midterm 2021-exo 3.2

by Marina Rapellini -
Hi
Thanks for your reply, but why is $f_0$ equal to $f_{-1}$ ?
Thank you
In reply to Marina Rapellini

Re: Midterm 2021-exo 3.2

by Thomas Weinberger -
Hi Marina,

Because for m = -1 and all n, we have that a_{m,n}=0, hence f_{-1}=\sum_{m \geq -1}\sum_n a_{m,n}\psi_{m,n}=\sum_{m \geq 0}\sum_n a_{m,n}\psi_{m,n}=f_{0}, see the sample solution.

Best,
Thomas