I want to find and display the polynomial equation for degree 1 and 2 using Newton Forward Divided Difference but the system deos not recognize when n == 3.

Supposedly when n = 3, the system will produce a polynomial equation for degree 2. the answer should be 0.5552 x^2 - 2.4446x + 3.6889.

Answer 1

[Subhajyoti]

Hi Azneen,

The “size” function returns a tuple of number of rows and columns present in the input data-matrix.

% Sample Data Table
c = [1.6, 1.2;
     1.9, 1.05;
     2.2, 1.0
    ]

c = 3x2

1.6000 1.2000 1.9000 1.0500 2.2000 1.0000

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n = size(c)

n = 1x2

3 2

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Now, when ‘n’ is compared with any scalar value, it performs an element wise comparison and return a Boolean vector (say, ‘b’). When ‘b’ is used in if-else conditional, it uses ‘all(b)’ to get a scalar Boolean value.

n == 3

ans = 1x2 logical array
   1   0

Here’s MATLAB code snippet to illustrate using ‘size’ function for data-matrix:

% Sample Data Table
c = [1.6, 1.2;
     1.9, 1.05;
     2.2, 1.0
    ];

[n, ~] = size(c)

n = 3

value = '';

if n==2
    D1 = (c(2,2) - c(1,2)) / (c(2,1) - c(1,1));
    a = D1;
    b = c(1,2) - (D1*c(1,1));
    value = sprintf('%.2f %+-.2f*x', b, a);
elseif n==3
    D1 = (c(2,2) - c(2,1)) / (c(2,1) - c(1,1));
    D2 = (c(3,2) - c(2,2)) / (c(3,1) - c(2,1));
    D3 = (D2 - D1) / (c(3,1) - c(2,1));

    a = D3;
    b = D1 - D3*(c(2,1)+c(1,1));
    c = (D3*c(1,1)*c(2,1))- D1*c(1,1) + c(1,2);
    value = sprintf('%.2f %+-.2f*x %+-.2f*x^2', c, b, a);
else
    value = 'THIS SYSTEM CAN ONLY FIND POLYNOMIALS DEGREE 1 AND 2 ONLY';
end

value

value = '32.76 -33.94*x +8.89*x^2'

Here, we are explicitly saving the first value of the tuple (number of rows in the data-matrix) into ‘n’. This gives us the desired conditional in the switch-cases.

For more details on the “size,” you can go through the following MathWorks documentation.

https://www.mathworks.com/help/matlab/ref/size.html

Hope the above information is helpful.