subject
Mathematics, 10.03.2020 09:00 drobledo9

. The following polynomials are the first five in the sequence known as Chebyshev polynomials of the first kind

T0(x)=1, T1(x)=x, T2(x)=2x2 −1 T3(x)=4x3 −3x, T4(x)=8x4 −8x2 +1.

(a) Show that {T0, T1, T2, T3, T4} is a basis for P4, the space of polynomials of degree ≤ 4.
(b) Check that differentiation defines a linear transformation TD : P4 → P3 and write down the matrix of each linear transformation in the Chebyshev basis. Similarly, check that integration is a linear transformation TS : P3 → P4.
(c) Let D and S be the differentiation and integration matrices, respectively, from part (b). Compute the matrix products DS and SD. Interpret the results using calculus: choose a suitable polynomial in P4, differentiate it, and then integrate it.
(d) Write down bases for the null spaces and column spaces of D and S. Provide the cor- responding polynomials. Can you interpret your results about D and S in light of what you know about differentiation and integration from calculus?

ansver
Answers: 3

Another question on Mathematics

question
Mathematics, 21.06.2019 15:00
Which expression is equivalent to 5r674 pression is equivalent to see lo 5r614) 4r322,4 ) 5 ( 2 5t5 |
Answers: 3
question
Mathematics, 21.06.2019 16:00
What kind of bond pays interest which is exempt from tax?
Answers: 1
question
Mathematics, 21.06.2019 18:40
Someone answer this check out the image!
Answers: 1
question
Mathematics, 21.06.2019 21:00
5x−4≥12 or 12x+5≤−4 can you with this problem
Answers: 3
You know the right answer?
. The following polynomials are the first five in the sequence known as Chebyshev polynomials of the...
Questions
question
Chemistry, 27.01.2021 01:00
question
Physics, 27.01.2021 01:00
question
Mathematics, 27.01.2021 01:00