For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a known mathematical function. The same function can then be used to compute true values at the interpolated points to use in error calculations. Consider the following mathematical function (Runge's function): RUNGE'S FUNCTION Write a function mfile that uses this formula to generate a set of data points. Your function should use those points along with the interpolation approaches outlined below to generate interpolated data (x_i, f_i) on a specified increment. Your function should accept the following inputs (in order): 1. A vector of x values at which f(x) is to be evaluated to generate the sampled data. 2. A scalar input specifying the increment to use for the interpolated data. Your function should use the following three approaches to generate interpolated data: • A polynomial of order (N-1) where N is the number of points in the sampled data . A linear spline . A clamped cubic spline with derivative end conditions set to values equal to the exact analytical derivative of f(x) evaluated at the end points. Your function should have the following three outputs (in order): 1. The interpolated data (f_i) generated with polynomial interpolation (column vector) 2. The interpolated data (f_i) generated with a linear spline (column vector) 3. The interpolated data (f_i) generated with the clamped cubic spline (column vector) Note this problem is similar to the humps interp.m example.
For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a known mathematical function. The same function can then be used to compute true values at the interpolated points to use in error calculations. Consider the following mathematical function (Runge's function): RUNGE'S FUNCTION Write a function mfile that uses this formula to generate a set of data points. Your function should use those points along with the interpolation approaches outlined below to generate interpolated data (x_i, f_i) on a specified increment. Your function should accept the following inputs (in order): 1. A vector of x values at which f(x) is to be evaluated to generate the sampled data. 2. A scalar input specifying the increment to use for the interpolated data. Your function should use the following three approaches to generate interpolated data: • A polynomial of order (N-1) where N is the number of points in the sampled data . A linear spline . A clamped cubic spline with derivative end conditions set to values equal to the exact analytical derivative of f(x) evaluated at the end points. Your function should have the following three outputs (in order): 1. The interpolated data (f_i) generated with polynomial interpolation (column vector) 2. The interpolated data (f_i) generated with a linear spline (column vector) 3. The interpolated data (f_i) generated with the clamped cubic spline (column vector) Note this problem is similar to the humps interp.m example.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a known mathematical
function. The same function can then be used to compute true values at the interpolated points to use in error calculations.
Consider the following mathematical function (Runge's function):
RUNGE'S FUNCTION
Write a function mfile that uses this formula to generate a set of data points. Your function should use those points along with the interpolation approaches outlined below to generate
interpolated data (x_i, f_i) on a specified increment. Your function should accept the following inputs (in order):
1. A vector of x values at which f(x) is to be evaluated to generate the sampled data.
2. A scalar input specifying the increment to use for the interpolated data.
Your function should use the following three approaches to generate interpolated data:
▪ A polynomial of order (N-1) where N is the number of points in the sampled data
▪ A linear spline
▪ A clamped cubic spline with derivative end conditions set to values equal to the exact analytical derivative of f(x) evaluated at the end points.
Your function should have the following three outputs (in order):
1. The interpolated data (f_i) generated with polynomial interpolation (column vector)
2. The interpolated data (f_i) generated with a linear spline (column vector)
3. The interpolated data (f_i) generated with the clamped cubic spline (column vector)
Note this problem is similar to the humps_interp.m example.
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