All Questions
Tagged with floating-point computational-complexity
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Fundamental Axiom of Floating Point Arithmetic for Complex Numbers Multiplication
I am trying to prove the fundamental axiom of floating point arithmetic also applies to complex number multiplication.
First, let $fl$ be a function that maps a number to its closest floating point ...
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What is the computational complexity of calculating determinants for matrices of finite precision floating-point numbers?
Following up from this older question, I understand that calculation of determinants for integer-valued matrices is possible with polynomial scaling. However, I have been unable to locate any ...
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Number of FLOPs for the inner and outer vector product?
I'm trying to educate myself on the relative cost of the cross and dot products relative to the number of floating point operations (FLOPs) each one requires. My understanding based on this paper (see ...
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Computer science FLOPs question (complexity): We have $100$ vectors, each with $10^5$ elements.
Our numerical analysis textbook has this problem:
How many bytes does it take to store $100$ vectors of length $10^5$? How
many flops does it take to form a linear combination of them (with $100$ ...
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What does the floating point arithmetic contribute to the rounding error in Mathematica?
I am a theoretical mathematician who works on the iterative method to find some generalized inverse of my interest. When I have tried some numerical example in Mathematica $11.0$, this does not ...
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Obtaining Coefficients of Powers of polynomial (e.g., $P(x)^N$) for large N, becomes Numerically Unstable
Obtaining Coefficients of Powers of polynomial (e.g., $P(x)^N$) for large N, becomes Numerically Unstable
I have a polynomial $P(x)$ where $-1\leq P(x) \leq 1$ for $-1 \leq x \leq 1$ and $-1\leq {\it ...
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Counting Iterations
How many multiplications are performed when the
following code fragment is executed? Express your answers in terms of $n$, where $n \geq 10$.
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How to calculate the inverse of sum of a Kronecker product and a diagonal matrix
I want to calculate the inverse of a matrix of the form $S = (A\otimes B+C)$, where $A$ and $B$ are symetric and invertible, $C$ is a diagonal matrix with positive elements. Basically if the ...
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How quickly can one compare exp(m/n) to a given rational?
For positive integers $\hspace{.06 in}m_{\hspace{.02 in}0}\hspace{.02 in},n_0\hspace{.02 in},m_1,n_1\:$, $\;$ how difficult is it to decide whether $$\exp\left(\hspace{-0.03 in}\frac{m_{\hspace{.02 in}...
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