Numerical Analysis Questions & Answers  
Question by Student 201327107
Professor, I don't understand about float type denormal number. I learned that denormal number condition is $$e=00000000$$then exponent should be $0-127$? But you explained exponent is $-126$. How comes?
09.21.16
The exponent of the denormal number is the same as the smallest exponent (-126) but the difference is with the significant which is 0.f instead of 1.f. Thus, the maximum denormal number is just below the minimum positive normal number. If the exponent would be -127, then there would be a large gap between the smallest positive normal number and the largest denormal number. Not a good thing! I liked your question, I'll give you 2 points bonus boost.
Question by Student 201327102
Professor, I have a question. In double type, you taught us that $$p=e-g$$$$g=\frac{{e}_{max}-1}{2}$$ And you substitute $${2}^{11}-1(e={11111111111}_{base 2})$$ for $${e}_{max}$$ then in $${p}_{max}={e}_{max}-g$$ we should use different value in $${e}_{max}(for{11111111111}_{base 2}-1)$$ Although e=11111111111 is not possible(because it indicates infinite # or NaN), why we use e=11111111111 in former $${e}_{max}$$ 'after all'? What's the matter that we use e=11111111111-1 in former $${e}_{max}?$$
09.22.16
I understand what is confusing you. When determining $g$, $e_\max$ refers to the maximum possible positive exponent. But in other cases it refers to the maximum possible positive exponent minus one (because the maximum positive exponent is reserved). They should have been written with 2 symbols in class to avoid confusion. In your notes, rewrite $e_\max$ to $e_\max^\prime$ when determining $p_\max$, with $e_\max^\prime=e_\max-1$. Good point, I'll give you 2 points bonus.
Question by Student 201029134
professor, I think you should give some interval like a to b in The Question#1 on your assignment but you just give initial point $x_{0}$. and I think it is same in The Question#3 So, I wonder whether it is right or not.
10.02.16
For A2Q3, there is no initial interval. For A2Q1, I have made a change to the question formulation. I'll give you 1.5 points bonus boost for pointing this out — I would have given more if you had not made spelling mistakes.
Question by Student 201029134
professor, I am sorry but I actually ask the question above this about the Question#2 not the Question#3. I think secant method need two points like $x_{0}$ and $x_{1}$ for calculating.
10.03.16
The secant method only needs one $x$ for the initial guess (it functions similarly to the Newton method). But you also need to specify a small $\Delta x$ initially to calculate the derivatives. Just set it to a small value of your choice: this won't affect much the convergence history as long as it is not too small.
Question by Student 201527151
Professor, when we use function of sin(x), we include<math.h> library and also write a function code of
double sin(double x){
    double ret;
    ret = sin(x);
    return ret;
}
. However, the code still doesn't work, and when I compile, it says: undefined reference to 'sin'. Is there something else we should add to a code about sin then?
10.04.16
I don't understand. Are you trying to code a sin(x) function? If so, there is no need to code it because the function sin(x) is already defined in the math library.
Question by Student 201129143
Professor, I wrote $$LX'=B$$ "Back substitution, but starting from top" on note. But another book say that this process is Forward substitution. So I wonder that what is the different.
10.10.16
You can call it forward substitution if you wish, this is the correct term. In class, I mentioned that this is the same process as back substitution (but going from top to bottom rather than bottom to top) to make it clear that this is not a new type of process. I'll give you 1.5 point bonus boost for sharing this with the class.
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