# Questions tagged [numerical-analysis]

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### Computing inverse matrix when an element changes

Given an $n \times n$ matrix $\mathbf{A}$. Let the inverse matrix of $\mathbf{A}$ be $\mathbf{A}^{-1}$ (that is, $\mathbf{A}\mathbf{A}^{-1} = \mathbf{I}$). Assume that one element in $\mathbf{A}$ is ...
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### Is 2**x faster to compute than exp(x)?

Forgive the naïveté that will be obvious in the way I ask this question as well as the fact that I'm asking it. Mathematicians typically use $\exp$ as it's the simplest/nicest base in ...
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### Overflow safe summation

Suppose I am given $n$ fixed width integers (i.e. they fit in a register of width $w$), $a_1, a_2, \dots a_n$ such that their sum $a_1 + a_2 + \dots + a_n = S$ also fits in a register of width $w$. ...
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### Floating point rounding

Can an IEEE-754 floating point number < 1 (i.e. generated with a random number generator which generates a number >= 0.0 and < 1.0) ever be multiplied by some integer (in floating point form) to ...
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### How to estimate floating-point precision of function?

Let's say I have a function that consists solely of floating-point operations where the last operation rounds the computed value to a predefined number of digits. And I feed this function with a range ...
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### Converge to unknown number with oracle

I'm playing a game where I'm trying to estimate an unknown real number $x$. An oracle exists that will answer the question of "Is a number $y$ greater than or equal to $x$?", to which the oracle will ...
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### Why aren't Grobner bases more common?

I have only heard of / seen Grobner bases in passing, but my understanding is that they are much like vector bases but for polynomials instead of linear systems. I know polynomials are used in CAD and ...
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