float_add

Error¶

Execute the two snippets below:

s=0; 
for n=999999:-1:1
 s+=1/(n*(n+1))
end
s

s=0; 
for n=1:999999
 s+=1/(n*(n+1))
end
s

Explain the difference.

Cancellation¶

Define $f(x)=\frac{1}{\sqrt{10^7+x}}-\frac{1}{\sqrt{10^7-x}}$ .
Plot it on the interval $[10^{-7},10^{-5}]$ .
Try to explain the phenomena.
Define a mathematically equivalent function that behaves correctly.

Represent¶

Define a function of the form tobin(a,b,d), that prints the first $d$ digits of the binary expansion of $\frac{a}{b}$ . Assume, that $a<b$ and they are integers.
Find the representation of $\frac{17}{36}$ and $\frac{9}{48}$ in the system $a=2,k_=-4,k_+=4,t=8$ .

Solve 2x2¶

Define a function of the form x=solve22(A,b), that computes the solution of the $Ax=b$ linear system, for $2\times 2$ , invertible matrices.

Back substitution¶

Define a function of the form x=lsolve(A,b), that computes the solution of the $Ax=b$ linear system, for quadratic, lower triangular matrices. You may assume, that $A$ is invertible.
Define a function of the form x=usolve(A,b), that computes the solution of the $Ax=b$ linear system, for quadratic, upper triangular matrices. You may assume, that $A$ is invertible.