# Tag Info

### In general, in a string of multiplication is it better to multiply the big numbers or the small numbers first?

If the numbers and the product are all "small" (magnitude less than $2^{63}$); the order doesn't matter at all; the multiplication will take time linear in the number of factors as it simply ...
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• 75.8k

### Calculate $\sum_{k=1}^{n} k\cdot\varphi(k)$

Found more powerful way of arranging, let $F(x)=\sum_{k \le x} k\cdot\varphi(k)$ $$\sum_{i \le x} i \cdot F(x/i) = x(x+1)(2x+1)/6$$  \implies F(x) = x(x+1)(2x+1)/6 \ - \sum_{2 \le i \le x} i \cdot ...
1 vote

• 8,055
1 vote

### In general, in a string of multiplication is it better to multiply the big numbers or the small numbers first?

We can assume that every single word multiplication takes some constant time, and that we need some algorithm to multiply n word by m word numbers. Now the answer depends on how fast this n by m word ...
• 8,724
1 vote

### Is non-convex optimisation really in NP class?

NP problems are decision problems, so an optimization problem would need to be restated as a decision problem. Instead of asking what value of $x$ minimizes a function, you would ask if there is a ...
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1 vote
Accepted

### What is the complexity of global solution of a nonlinear system?

In the worst case, $F_j=0$ for all $j$, and then there are at least $2^n$ roots. Obviously any method to print all roots must take time at least equal to the number of roots, so this proves that the ...
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