Purchase Solution

Inner Product, Linear Space, Constant Polynomial and Mean Square Deivation

Not what you're looking for?

Ask Custom Question

Let C[1,3] be the (real) linear space of all real continuous functions on the closed interval [1,3], equipped with the inner product defined by setting

<f,g> := 1&#8747;3f(t)g(t)dt, f,g E C[1,3].

Let f(t) = 1/t, t E [1,3].

(i). Show that the constant polynomial g which best approximates f on [1,3] (in the sense of least squares) is given by
g(t) = ½ ln3, t E [1,3].

Find the mean square deviation ||f-g||2.

(ii) Find the best linear polynomial approximate to f on [1,3] and calculate the corresponding mean square deviation.
---

(See attached file for full problem description and accurate equations)

Attachments
Purchase this Solution

Solution Summary

Inner Product, Linear Space, Constant Polynomial and Mean Square Deivation are investigated. The solution is detailed and well presented.

Purchase this Solution


Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.