> 1. Can we have tables instead of figures for the matlab results?

Yes, but in a paper figures are usually more impressive and easier for a reader to grasp quickly.

In many, many papers, a little arithmetic on the numbers in tables shows that they are inconsistent and there is some mistake somewhere. Don't let this be the case with your figures!


> 2. Do we need to do matlab validation for all problems? For
> example I cannot imagine a feasible way to validate problems 1.3
> and 2.6.

To check your result for 1.3, generate many vectors (x1 ... xn). Select those that have SUM xi within some narrow range. Now plot the
distribution of x1 from the selected vectors. Alternatively, plot the mean and variance of x1 as a function of SUM xi.

For 2.6, I agree, I can't think of a numerical validation immediately.

> 3. Do we have to do goodness of fit validation for e.g. problem
> 1.1 (that would validate how well the numerical results match
> the solution)?

No, intuitively plausible validations are sufficient. You don't need to do a whole second level of statistics, to check goodness of fit.

In general, people get too stuck on cookbook recipes for significance testing. This is important, but it is even more important to gain real insight and to focus on results that have practical significance, which usually means results that are far stronger than merely statistically significant. Also, significance testing is always based on assumptions that are usually not precisely true. So p-values, confidence intervals etc. are usually not numerically correct.