# Questions tagged [machine-precision]

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### verifying Ramanujan constant

The famous Ramanujan constant $e^{\pi \sqrt{163}}$ is a near-integer. see the link here. I tried to calculate this number with matlab and failed. Matlab cannot even deliver the first 9 apparently ...
• 1,084
1 vote
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1 vote
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### Rounding in floating point operations

I'm given this set of floating point numbers: And I'm given the function: I'm then asked to find the value of f for: So I've done this: Now my guess is that I need to convert the exact value (1....
• 53
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### Given an analytic function can I derive to what precision I need to evaluate its arguments to get a result of a given precision?

Suppose I have some arbitrary analytic function over the reals e.g.: $$x \mapsto \frac{\sqrt{\sin(x)+2e^x}}{x^2 - \ln(x^x)}$$ Given some input of arbitrary precision $x$ how can I evaluate such an ...
• 113
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### Exponencial mantissa

I try to compute a function of type $e^x$. Since its natural fast-growing behaviour, the most natural behaviour is to decompose the resulting number into its mantissa and exponent components. However, ...
• 496
1 vote
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### Why is this function not being graphed as expected?

I am interested in the Rastrigin function: https://en.wikipedia.org/wiki/Rastrigin_function. I have read that the local minimums of this function occur at integer coordinates. However, when I plug ...
• 128
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### Finding a machine number such that $fl(x)=x(1+\delta)$.

The guide book asks me for A real number $x$ in range of a machine with $\beta=2$ (binary) and $n=24$ (24 mantissa positions), such that it satisfy $fl(x)=x(1+\delta)$, with $|\delta|$ as big ...
2k views

### Machine epsilon: why is $(1 + \epsilon) + \epsilon = 1$?

My book on real analysis has the following statement: I don't understand how the first equation can possibly be true, by definition of machine epsilon. Machine epsilon is defined as the smallest ...
1 vote
82 views

### How to Calculate the Precision Required to Exactly Produce the Repeating Sequence of Digits in the Decimal Expansion of a Fraction

Say I am given a fraction $\frac{p}{q}$ and wish to express it as a decimal such that the repeating sequence of digits is accurately displayed at least once and preferably twice in the printed output. ...
• 2,623
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### Tough test polynomials for (finite precision) complex root finding methods, especially Aberth's method

Today I have implemented Aberth's method for complex polynomial root finding. And I have to say I am enchanted about its astonishing performance and its intriguing simplicity. Before I go on believing ...
• 365
1 vote
350 views

### Floating-point rounding error in numerical differentiation formula

In Numerical Analysis by Timothy Sauer (Pearson, 2nd Edition) it says that $\tilde{f'}(x+h) = f(x+h) + \epsilon_{\text{mach}}$, where $\tilde{f'}(x)$ is the floating-point representation of the given ...
• 647
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### Finding the real roots of a univariate polynomial on the interval [0,1]

I have numerous, univariate polynomials with degree in excess of 100 and with very, very large coefficients (Here's an example coefficient ...
• 287
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### Calculator Confusion using Windows and Androids

I just came across this calculation, it's really confusing. I ran the following calculations in windows and android calculators. $1/98\cdot 98 = 1$ $1/98 = 0.0102040816326531$ \$0.0102040816326531 * ...
• 123
1 vote