Advantages over what? For what?
Generally linear interpolation is done because one infers that the relationship between points is linear and/or it is the the easiest kind of interpolation. In the absence of data or theory to help you infer the relationship between points the principle of parsimony suggest that use the simplest that gets the job done - linear.
The process is called interpolation, which applies a computed formula of the line to a given x or y value. (More specifically, it is "linear interpolation".)
For a linear I can see no advantage in the table method.
The results are more reliable for interpolation .
Interpolation.
Interpolation
Linear interpolation is used as a method used in mathematics of constructing a curve that has the best fit to a series of points of data using linear polynomials.
Interpolation in general is a way to determine intermediate values from a set of coordinates. Linear interpolation would be to fit a single linear function to the entire set of coordinates. Piecewise linear interpolation would then be to determine intermediate values from the set of coordinates by fitting linear functions between each set of coordinates. Connect-the-dots so to speak.
pu = p0 + u(p1 - p0)
The bisection method is simpler to implement and guarantees convergence to a root if one exists within the initial interval, but it can be slower as it always halves the interval. In contrast, linear interpolation converges faster but does not guarantee convergence, and it might fail if the function is not well approximated by a linear model in the interval.
The process is called interpolation, which applies a computed formula of the line to a given x or y value. (More specifically, it is "linear interpolation".)
What you are asking is not precisely clear, but in general missing data is filled in by a process of interpolation. eg. Linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
advantages and disadvantages of linear model communication
Linear Interpolation (Statistics) Below is a Frequency Table of the Lengths, to the nearest minute, of phone calls made from an office one day.Length (min)-----------------Frequency0 - 2 --------------------------------- 83 - 5 --------------------------------- 116 - 9 --------------------------------- 1610 - 15 ----------------------------- 1416 - 20 ------------------------------ 9> 20 ---------------------------------- 3
basically linear is easier than iterativ
Suppose you know the density of some (strange) substance at 10oC and 20oC, 125 gm/cm3 and 145 gm/cm3. You want to know its density at, say, 13oC. You could use linear interpolation. To do so, you first find the linear function that satisfies the points (10, 125) and (20, 145). I think it's D=105 + 2t. Now since 13 is between the temperatures for which we have data we can interpolate: 105 + 2(13) = 131 or 131 gm/cm3.
For a linear I can see no advantage in the table method.
Matlab has a lot of functions for interpolate, depending on what you're trying to do. You don't need a toolbox for it, either. Type "doc interp1" to get started and navigate the help file from there.