numerical-analysis

The DBL_EPSILON/std::numeric_limits::epsilon will give me the smallest value that will make a difference when adding with one. I'm having trouble understanding how to apply this knowledge into something useful. The epsilon is much larger than the smallest value the computer can handle, so It would seem like a correct assumption that its safe to use smaller values than epsilon? Should the ratio between the values I'm working with be smaller than 1/epsilon ? AProgrammer The definition of DBL_EPSILON isn't that. It is the difference between the next representable number after 1 and 1 (your

I'm wanting to find the number of mantissa digits and the unit round-off on a particular computer. I have an understanding of what these are, just no idea how to find them - though I understand they can vary from computer to computer. I need this number in order to perform certain aspects of numerical analysis, like analyzing errors. What I'm currently thinking is that I could write a small c++ program to slowly increment a number until overflow occurs, but I'm not sure what type of number to use. Am I on the right track? How exactly does one go about calculating this? I would think that

I would like to ask a question regarding single channel image interpolation. Single channel is chosen just for simplicity otherwise I'm working on multiple channel images. Assume there is a single channel image with pure black background ( pixel intensity 0) on which there are some pixels with non-zero intensity values. I want to apply an interpolation algorithm to fill the entire black area of the image with interpolated values coming from the neighboring non-zero intensity pixels. What interpolation algorithm would you recommend for a smooth interpolation applicable to this problem? As

I'm trying to implement Runge-Kutta for example problems dy/dt = y - t^2 + 1 and dy/dt = t * y + t^3 in C# and I cannot seem to get the output I'm expecting. I have split my program into several classes to try and look at the work individually. I think that my main error is coming from trying to pass a method through the Runge-Kutta process as a variable using a delegate. Equation Class: namespace RK4 { public class Eqn { double t; double y; double dt; double b; public Eqn(double t, double y, double dt, double b) { this.t = t; this.y = y; this.dt = dt; this.b = b; } public void Run1() { double

I am curious to know what algorithm R's mean function uses. Is there some reference to the numerical properties of this algorithm? I found the following C code in summary.c:do_summary(): case REALSXP: PROTECT(ans = allocVector(REALSXP, 1)); for (i = 0; i < n; i++) s += REAL(x)[i]; s /= n; if(R_FINITE((double)s)) { for (i = 0; i < n; i++) t += (REAL(x)[i] - s); s += t/n; } REAL(ans)[0] = s; break; It seems to do a straight up mean: for (i = 0; i < n; i++) s += REAL(x)[i]; s /= n; Then it adds what i assume is a numerical correction which seems to be the mean difference from the mean of the data