The following are some recommended conceptual self-assessment questions for the lesson called Linearizing the parametric functional model. They’re intended for you to work through to test your own understanding of the key concepts we covered there.
a) What is ?
b) What is each term called and what does each term mean?
c) What is the equation for each term?
d) What dimensions does each term have?
e) Which term is most dependent on Taylor’s Theorem?
f) Why is the equation in a) so important?
In Example 1 of the video accompanying this topic, we treated point B as having unknown coordinates and point A as having known coordinates, i.e. where the number of unknowns = 2.
Derive the equations for each term in the matrix for the more general case where the coordinates of point A are also unknown, i.e. where the number of unknowns = 4. You don’t need to compute the numerical values here. Just take the partial derivatives required and provide the equations you would use for computing the numerical values for each spot in the 1 x 4 matrix.
If you have the following functional model:
a) Is it linear or non-linear in ? Explain.
b) What is the corresponding equation for each row of the design matrix ?
You can click through to other self-assessments or lessons (if any) using the button below, and return here whenever you wish.