Indexing polynomials using 'for' loop

I need help about an exercise that I've been given from my professor. Six polynomials are given:

• p1 = [0 2 0 -2 6 -1]; % the first polynomial is p1(x)=2x^4-2x^2+6x-1
• p2 = [1 3 0 -2 0 0]; % the second polynomial is p2(x)=x^5+3x^4-5x^2
• p3 = [0 0 3 1 0 -10]; %...
• p4 = [0 0 0 -4 16 -5]; %...
• p5 = [1 -1 0 1 0 -1];
• p6 = [3 -12 0 0 0 7];

Using 'polyval(p(i),2/3)' function I should create new vector 'A' that contains all the values of the polynomials from 'p1' to 'p6'(i=1:6) for x=2/3. Then find the minimum and maximum value of the vector. I want to know how can I loop through the polynomials to find their value and put that value in the new vector. Thank you in advance.

Answer 1

[Mohammad Abouali]

%%Solution 1: (not recommended)
p1 = [0 2 0 -2 6 -1];
p2 = [1 3 0 -2 0 0];
p3 = [0 0 3 1 0 -10];
p4 = [0 0 0 -4 16 -5];
p5 = [1 -1 0 1 0 -1];
p6 = [3 -12 0 0 0 7];

polyValue=zeros(6,1);
for i=1:6
  polyValue(i)=eval(sprintf('polyval(p%d,2/3)',i));
end

fprintf('Solution 1:(not recommended)\nmin: %f, max: %f.\n',min(polyValue),max(polyValue));

%%Solution 2: 
p  = [0 2 0 -2 6 -1; ...
      1 3 0 -2 0 0; ...
      0 0 3 1 0 -10; ... 
      0 0 0 -4 16 -5; ...
      1 -1 0 1 0 -1; ...
      3 -12 0 0 0 7];

polyValue=zeros(6,1);
for i=1:6
  polyValue(i)=polyval(p(i,:),2/3);
end

fprintf('Solution 2:\nmin: %f, max: %f.\n',min(polyValue),max(polyValue));

Once you run it you get this results:

Solution 1:(not recommended)
min: -8.666667, max: 5.024691.
Solution 2:
min: -8.666667, max: 5.024691.

As you can see the difference between the solutions is slightly how the polynomial coefficients are stored.

[Blazo Arsoski]

You helped me a lot. Thank you sir.

[Mohammad Abouali]

you are welcome

[Stephen23]

@Blazo Arsoski: and please note the advice that solution one is "not recommended" dues to relying on eval. Read more to know why:

http://www.mathworks.com/matlabcentral/answers/196952-how-to-create-new-variables-in-batches-with-strcat