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smallest poisitive integer does not belong in floating point system F

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#number-systems #floating-point
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Finding a machine number such that $fl(x)=x(1+\delta)$.

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#numerical-methods #floating-point #machine-precision
577
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$\exp(-i \infty)$ is "Not a Number" according to MATLAB. Why?

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#complex-numbers #exponential-function #matlab #floating-point
253
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Relative error floating point number multiplication/division

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#numerical-methods #numerical-linear-algebra #floating-point #numerical-calculus
48
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Convert $x/y \cdot \frac{1-\delta_1-\delta_3}{(1-\delta_2)}$ to $x/y \cdot (1-\delta)$ using calculus

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#calculus #infinitesimals #floating-point #rounding-error
728
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Question about machine epsilon

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#computer-science #floating-point
205
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Topological nature of IEEE floating-point numbers

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#general-topology #continuity #floating-point #topological-semigroups
1.8k
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Floating point arithmetic — catastrophic and subtractive cancellation

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#floating-point #catastrophic-cancellation
63
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For rational numbers $a, b$, what is the range of $b$ such that $\lceil a + b \rfloor = \lceil a \rfloor$ holds?

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#floating-point #rounding-error
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Show that formula is backwards stable

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#numerical-methods #floating-point
7.1k
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Minimum number of bits to represent negative number

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#arithmetic #integers #computational-mathematics #binary #floating-point
19
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How many discrete points can be expressed in $[-1/2, 1/2)$with IEEE 754 double floats and what is the meaning of precision?

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#floating-point
430
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Why is $0.09 + 0.01$ not exactly representable as $0.1$ in floating-point systems but $0.085 + 0.015$ is?

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#binary #floating-point
326
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Floating point and LU decomposition

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#numerical-linear-algebra #floating-point
120
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Rounding in floating point operations

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#floating-point #machine-precision

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