LagrangePolynomials

# LagrangePolynomials - Lagrange interpolating Polynomials...

This preview shows pages 1–2. Sign up to view the full content.

Lagrange interpolating Polynomials James Keesling 1 Determining the Coefficients of the Lagrange Interpolat- ing Polynomial by Linear Equations It is frequently the case that we will have certain data points, { ( x 0 , y 0 ) , ( x 1 , y 1 ) , . . . , ( x n , y n ) } , and will want to fit a curve through these points. In this chapter we will fit a polynomial of minimal degree through the points. We assume that the points { x 0 , x 1 , . . . , x n } are all distinct. In that case we can fit a polynomial of degree n (or possibly less) through the points. If we write the polynomial in the following form, then we can use the points to determine the coefficients. L ( x ) = a 0 + a 1 · x + a 2 · x 2 + · · · + a n · x n y 0 = a 0 + a 1 · x 0 + a 2 · x 2 0 + · · · a n · x n 0 y 1 = a 0 + a 1 · x 1 + a 2 · x 2 1 + · · · a n · x n 1 . . . y n = a 0 + a 1 · x n + a 2 · x 2 n + · · · a n · x n n We can solve these equations using matrices. The vector A = a 0 a 1 . . . a n is the set of coefficients to be determined. We let M = V [ x 0 , x 1 , . . . , x n ] be the Van- dermonde Matrix and B

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern