Questions tagged [error-estimation]
The error-estimation tag has no usage guidance.
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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 ...
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Compile-time error control vs. interval arithmetic?
I use interval arithmetic for reliable computing. Now, a procedure coded in a good implementation of interval arithmetic takes perhaps about eight times as much as the same procedure carried out ...
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Numerical Stability of Halley's Recurrence for Integer $n^{\mathrm{th}}$-Root
tl;dr? See last paragraph.
If I use the initial value $2^{\left(\big\lfloor\lfloor\log_2 x \rfloor/n\big\rfloor + 1\right)}$ with Halley's recurrence in the compact form
$ x_{k+1} = \frac{x_k\Big[A\...
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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,...
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Algorithm for finding relative estimate from absolute estimate
I am trying to find a textbook reference for an algorithm that gives you a relative estimate of a quantity $a$ (i.e. $|a-\overline{a}|\leq \epsilon_{rel} a$) from an algorithm that gives you an ...
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Computing the error bound of floating-point expression
How should I compute the maximum absolute and relative error of the following IEEE-754 floating-point expression?
a.y + (x - a.x) * ((b.y - a.y) / (b.x - a.x))
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How to calculate error bounds for the function behind the following algorithm?
D.E. Knuth, in his infamous The Art of Computer Programming, section 1.2.2, presents the following algorithm to efficiently calculate logarithms based on the method used by Henry Briggs:
Suppose that ...
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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 ...
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Q-Learning Error Bounds
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 ...
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