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In general, cubic interpolation is better than linear interpolation in most aspects such as smoothness of the function and higher accuracy in approximating the original function. However, there is at least one aspect where linear interpolation is better: the linear interpolation will not produce the "overshoot" situation.
I suppose you get something like 0.5098 from the suggested method. There are two reasons why this 'linear interpolation' method may not give an exact answer: (a) tables are rounded to 4 (maybe 5) places, so there is some rounding error, (b) the normal curve is 'almost' linear over such a short distance, but it is really a curve, not a line.
There's a linear interpolation (by computing fractions), but my recent try on logarithmic interpolation sometimes produces worse results than the linear one. Disappointing. First I tried to follow Link which was a disaster.
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You get a system of linear equations in which the unknowns are the coefficients of the polynomial pieces. The system of equations is nicely "banded", and therefore easy to solve. For further details, see here , or here , or this answer .
For 10,000, Kelly purchases an annuity−immediate that pays 400 quarterly for the next 10 years. Calculate the annual nominal interest rate convertible monthly earned by Kelly’s investment.
2. I'll show how to compute the value of the linear interpolation with correct rounding; i.e. as if the linear interpolation were computed with exact arithmetic and then rounded. First represent the linear interpolation as a + tb − ta. Using the exact product from Pedro Gimenos answer, decompose tb = c0 +c1.
To linearly interpolate between two points p1 p 1 and p2 p 2 in 3D-space, I can calculate: pt =p1 + t(p2 −p1) p t = p 1 + t (p 2 − p 1) where t t is a parameter 0 ≤ t ≤ 1 0 ≤ t ≤ 1. Is there any representation of rotation that would allows shortest-path interpolation using this function (with appropriately defined addition ...
But the linear interpolation computation is basically taking a proportion, so no more difficult using pencil and paper than a division and two subtractions. You also then evaluate the function at the new argument, assuming you are trying to refine the root approximation to a given accuracy. $\endgroup$
This 2D image needs to be down-sampled using bilinear interpolation to a grid of size PxQ (P and Q are to be configured as input parameters) e.g. lets take PxQ is 8x8. And assume input 2D array image is of size 200x100. i.e 200 columns, 100 rows. Now how while performing downsampling using bilinear interpolation of this 200x100 image, should I ...