Tagged Questions

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Best approximating linear polynomial for $|x|$ on $[-1,5]$ [on hold]

How to find the best approximation polynomial $p_1(x)\in P_1$ for $|x|$ on $[-1,5]$ w.r.t. $\|\cdot\|_{\infty}$? I want to use the Equioscillation theorem but have no clue.
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Changing the order of the elements of the divided difference Polynomial Interpolation

Apparently this is rather trivial but I don't understand why what I've highlighted in green is correct.
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How can I cleverly use the error term of polynomial interpolation?

Let $f(x):=x^2$. We're interested in the closed form of the error $|I(f)-T_n(f)|$ where ...
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Determine the coefficients of a polynomial knowing its roots

My prof. gave this problem as a bonus in an exam, and I couldn't figure out a solution. Some hints or a general method of solving it would be very nice. Given the following polynomial: ...
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What is the Most Efficient Way to Calculate the Internal Rate of Return?

I have built a program that prices financial assets and it does this in part by calculating the IRR. The problem is that it does not run as quickly as I would like it to. I currently use the ...
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Derivation of composite Gaussian quadrature error formula

I am working on studying for the Numerical Analysis qualifying exams. One of the questions I am stuck on is the following: Derive the error term for the composite Gaussian quadrature rule with ...
I have a pair of rational polynomial fractions $\frac{A(x)}{B(x)} + \frac{C(x)}{D(x)}$ where A, B, C, and D are all polynomials in x, and I have their coefficients as an array of numbers. I would ...