Tagged Questions

Questions on interpolation, the estimation of the value of a function from given input, based on the values of the function at known points.

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How to find the intersection of a line and a plane with interpolation ( given two points in the opposite side of the plane)

I have two points in the opposite side of a plane (P1,P2) in 3D space, and i know their signed distances to the plane(D1,D2). how can i use interpolation to calculate the point that is the ...
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How to resample translated grid to ensure consistent interpolation?

I have a grid of values, sampled at certain locations. I'd like to translate grid by some offset and resample it. The questions is: what should be the resampling and interpolation formulas such that ...
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When fitting a polynomial to data points, how to determine the reasonable degree to use?

I have wondered the following: Suppose that there is a set of data points $(x_i,y_i)$. Then I would like to know if it is more reasonable to assume if there is a polynomial relation of degree $m$ ...
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How does one derive Runge Kutta methods from polynomial interpolation?

In some numerical analysis classes, a neat way of deriving the Adams-Bashforth and Adams-Moulton methods is to approximate the function by a polynomial, and integrate the polynomial analytically over ...
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Find the approximation for the interpolation of $f(x)$ by a polynomial of second degree

Assume that $f(x)$ has a minimum in the interval $x_{n-1}\leq x\leq x_{n+1}$ where $x_k=x_0+kh$, $k$ being an integer. Show that the interpolation of $f(x)$ by a polynomial of second degree yields the ...
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Should I use interpolation when finding median, and quartiles?

I am a S1 maths (Edexcel) AS student in the UK. My question: Say we have a stem-and-leaf diagram with 26 values. We want to find the lower quartile. To get the marks for our specification, we need to ...
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Why polynomial interpolation is considered as better than others?

Why polynomial interpolation is considered as better than others? In case of interpolation, the function $\phi(x)$ to approximate the unknown function $f(x)$ may be polynomial, exponential, ...
So i was given this question Given the following data pairs, find the interpolating polynomial of degree 3 and estimate the value of y corresponding to x = 1.5. a) $(0, 1), (1, 2), (2, 5), (3, 10)$ ...
Does there exist smooth or $C^2$ function for some infinite given points $a(n)$?
I know that there exist some smooth function (polynomial) for finite numbers of values. The question is if there exists function (not necessary unique) which is twice differentiable and $f(n)=a(n)$?