Prove the least squares approximation property of Legendre polynomials [see (9.5) and (9.6)] as follows. Let
Show that the Legendre series for
Write the quadratic polynomial satisfying the least squares condition as
’s are normalized, and others are equal to the coefficients
Add and subtract
Now determine the values of the
’s to make
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Mathematical Methods in the Physical Sciences
Additional Math Textbook Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Introductory Combinatorics
Introductory Mathematics for Engineering Applications
Mathematics for Elementary Teachers with Activities (5th Edition)
Mathematics All Around (6th Edition)
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage