# Questions tagged [error-estimation]

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### Is the per-vertex error over a PageRank iteration monotonically decreasing?

It seems to me that taken over the entire graph, the norm of the error vector must be monotonically decreasing, otherwise we couldn't guarantee that PageRank would ever converge. However, is the same ...
383 views

### Is order of matrix multiplication affecting numerical accuracy of the result?

I have to multiply three matrices of floats: A (100x8000), B (8000x27) and C (27x1). Is ...
197 views

### What is the state of the algorithmic art for floating point arithmetic on complex numbers?

Most modern compilers and processors implement the IEEE 754 binary formats for floating point numbers. IEEE 754 guarantees that the addition, subtraction, multiplication, division, and square root ...
195 views

### What does $\tilde{O}_P(N^\alpha)$ mean?

What does $\tilde{O}_P(N^\alpha)$ mean? It appears in an estimation error mention in this paper, in the second paragraph on page 3. What does big O subscript P mean in a probability context?
457 views

### Proof that (x-y)(x+y) is more accurate than x²-y²

I was carrying on my reading of What Every Computer Scientist Should Know About Floating-Point Arithmetic but got stuck on the proof of Theorem 2 (page 34). At some point it says: \begin{align} (x \...
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### Representing Computations on Transcendental Numbers

Consider the set of transcendental numbers that are not compressible to a finite base-2 representation. How can I compute multiples (more generally, any algebraic computation) of one of these numbers,...
80 views

### How do compilers assure stability?

Suppose you need a c compiler. It would be preferable to write that compiler in a c-like language, given the complexity of a compiler of that degree. At best, the c compiler would be written in c, but ...
686 views

### Avoiding overflows while computing $e^x$ by Taylor series

I'm coding a program to calculate the value of $e^x$ by using the Taylor expansion, that is: $$e^x =\sum_{k=0}^\infty \frac{x^k}{k!}$$ ...
157 views

### What happens to a file after too many copy-pasting?

Let's say we're talking about a 1 GB video file. It's copy-pasted from hard disk D1 to the hard disk D2, then from D2 to D3, and so on, all using Windows. If we continue this process for like 1 ...
2k views

### 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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### Double Write After Write Dependency in out-of-order/in-order executions

What is going to happen when we have a WAW(write after write) dependency which consists of two consecutive WRITE instructions into the same register. We know we can solve a simple WAW dependency by ...
24 views

### minimal distance of a self correcting code

i wonder: how can i find minimal distance of a self correcting code in following situation: if we know that a code can fix every 3 errors(if not more than 3 errors, the word is recovered) and can ...
I have searched a lot for this, but apparently there is no result on calculating any bound on the error $||Q-Q^*||$ when I stop Q-learning after say $N$ iterations ($Q$ is the vector of Q-values at ...