Systems Series Transforms

Question 1

How many collocation points does the Interpolating Polynomial P_N(x) have?

Answer 1

N+1

x_0, …, x_N

Question 2

Infinity norm of g(x)

Answer 2

max x |g(x)|

in [a,b]

Question 3

How many zeros for chebshev polynomial C_n(x)

Answer 3

n

Question 4

Condition for Gram-Schmidt Orthogonalisation on a set of functions

Answer 4

Set of functions must be

LINEARLY INDEPENDENT

Question 5

Primitive matrix

Answer 5

for some k, A^k has only +ve entries

Question 6

All matrix entries of ‘A’ are >= 0 implies…

Answer 6

the eigenvalue of A of max magnitude is real and +ve

Question 7

Difference between Markov & Population Projection Matrices

Answer 7

Columns don’t have to sum to 1 in Population Projection Matrices