Do we have to setup all 3n equations for the n quadratic splines for (n+1) data points?

QUESTION ASKED BY STUDENT: For linear splines, we still find each line individually. In quadratic, we are forced to find every equation at once, correct? Which is where the matrix comes from?

ANSWER: That sounds right, but one can find quadratic equations individually also .
How?
If the first spline is linear, then that spline can be found by the two points it goes through.
Then the second spline goes thru two points, and that gives two equations.  The slope of the second spline is same as the slope of first spline at the common interior point, and the first spline is known. This gives the third eqn.  This process can be repeated for each following spline.

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This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos.  Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

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Checking if a number is non-negative or not?

Many students ask me how do I do this or that in MATLAB.  This is a new addition to the “How do I do that in MATLAB“  series.
 
In this blog, I show you how to use the if-else-end statement to write a simple program of finding if a number is non-negative or not.
 
Here are the links for the program.
The mfile is here
The published version of the mfile is here
 

%% HOW DO I DO THAT IN MATLAB SERIES?
% In this series, I am answering questions that students have asked
% me about MATLAB.
%% TOPIC
% How do I check if a number is non-negative or negative
%% SUMMARY
% Language : Matlab 2010a;
% Authors : Autar Kaw and Sri Harsha Garapati;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/if_else_end_statements_blog.m
% Last Revised : January 23, 2012;
% Abstract: This program shows you how to check if a number is negative or
% non-negative using if-else-end statement in MATLAB
clc
clear all
%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to check if a number is negative or’)
disp(‘   non-negative using if-else-end statement in MATLAB’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar Kaw and Sri Harsha Garapati of https://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://numericalmethods.eng.usf.edu/blog/if_else_end_statements_blog.m’)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   February 13, 2012’)
disp(‘ ‘)

%% INPUTS
 
% Enter the number to be tested
a=4;
%% DISPLAYING INPUTS
disp(‘  ‘)
disp(‘INPUTS’)

% Printing the input number
fprintf(‘The input number to be tested is %g\n’,a)
%% CODE AND DISPLAYING OUTPUT
disp(‘  ‘)
disp(‘OUTPUTS’)

% using the if-else-end statement to check
if (a>=0)
    disp(‘The number is nonnegative’)
else
    disp(‘The number is negative’)
end

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This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos.  Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.