interpolation-lecture

# interpolation-lecture

This preview shows pages 1–7. Sign up to view the full content.

Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Scientific Computing: An Introductory Survey Chapter 7 – Interpolation Prof. Michael T. Heath Department of Computer Science University of Illinois at Urbana-Champaign Copyright c 2002. Reproduction permitted for noncommercial, educational use only. Michael T. Heath Scientific Computing 1 / 56 Selected subset of slides for CS 357 - page numbers will not necessarily be correct

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

View Full Document
Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Outline 1 Interpolation 2 Polynomial Interpolation 3 Piecewise Polynomial Interpolation Michael T. Heath Scientific Computing 2 / 56
Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Motivation Choosing Interpolant Existence and Uniqueness Interpolation Basic interpolation problem: for given data ( t 1 , y 1 ) , ( t 2 , y 2 ) , . . . ( t m , y m ) with t 1 < t 2 < · · · < t m determine function f : R R such that f ( t i ) = y i , i = 1 , . . . , m f is interpolating function , or interpolant , for given data Additional data might be prescribed, such as slope of interpolant at given points Additional constraints might be imposed, such as smoothness, monotonicity, or convexity of interpolant f could be function of more than one variable, but we will consider only one-dimensional case Michael T. Heath Scientific Computing 3 / 56

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

View Full Document
Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Motivation Choosing Interpolant Existence and Uniqueness Purposes for Interpolation Plotting smooth curve through discrete data points Reading between lines of table Differentiating or integrating tabular data Quick and easy evaluation of mathematical function Replacing complicated function by simple one Michael T. Heath Scientific Computing 4 / 56
Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Motivation Choosing Interpolant Existence and Uniqueness Interpolation vs Approximation By definition, interpolating function fits given data points exactly Interpolation is inappropriate if data points subject to significant errors It is usually preferable to smooth noisy data, for example by least squares approximation Approximation is also more appropriate for special function libraries Michael T. Heath Scientific Computing 5 / 56

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

View Full Document
Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Motivation Choosing Interpolant Existence and Uniqueness Issues in Interpolation Arbitrarily many functions interpolate given set of data points What form should interpolating function have? How should interpolant behave between data points? Should interpolant inherit properties of data, such as monotonicity, convexity, or periodicity? Are parameters that define interpolating function meaningful?
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