Incorrect calculations: polynomials
Caleb Zhao

Caleb Zhao @zaim

About: Numerical analyst focused on computational error reduction and simulation accuracy.

Location:
Shanghai, China
Joined:
Oct 26, 2024

Incorrect calculations: polynomials

Publish Date: Nov 6 '24
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In this blog post, we discuss incorrect calculations of polynomials in MATLAB.

Example 1. Given that

f(x)=727313x1289459499x1144x2+665683.13 f(x)=727313\,x^{12}-89459499\,x^{11}-44\,x^2+665683.13
and
g(x)=584927x9721800000x8+101188x713x2+19795832, g(x)=584927\,x^9-721800000\,x^8+101188\,x^7-13\,x^2+19795832\,,

calculate f(123)f(123) and g(1234).g(1234)\,.

Let's just post the figure directly.

MATLAB outputFrom the above screenshot, it can be seen that the two outputs from MATLAB are both large numbers, with one having 16 integer digits and the other having 17 integer digits.

However, the accurate values of the two polynomials are 7.13 and 4, respectively (as provided by ISRealsoft). Thus, the outputs from MATLAB are both incorrect.

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