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Questions tagged [precision]

Issues related to the representation of numerical quantities in a finite representation in a given base differing from their exact mathematical value.

7 questions with no upvoted or accepted answers
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Updating matrix diagonal with Woodbury matrix identity and maintaining numerical accuracy

I have a dense matrix A and its corresponding inverse $A^{-1}$. The Woodbury matrix identity states: $$ (A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1} + VA^{-1}U)^{-1}VA^{-1} $$ I wish to perform small ...
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47 views

Evaluate Nth root of a rational to a correctly rounded float

Excuse my lack of vocabulary for I have no formal training in this field, which is also why I ask this question - it may be trivial or it may be impossible. I want to evaluate an expression in the ...
4
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0answers
108 views

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 ...
1
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81 views

How to compute large condition number of a matrix in Python?

I have a matrix that is extremely singular, but I am still interested in computing the exact condition number, which is the ratio between the largest and smallest singular values. Is it possible to ...
1
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0answers
149 views

Numerical Precision in Matrix Inversion Routines

Let's say I have a matrix $\mathbf{A}\in\mathbb{R}^{n\times n}$, and its associated inverse, $\mathbf{A}^{-1}$. The elements of $\mathbf{A}$ are given in IEEE single precision, i.e. 23-bit mantissa, ...
1
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75 views

Computing the change of function at two close points without cancellation

I want to compute the difference $\Delta f(x_1,x_2) = f(x_1)-f(x_2)$ of a smooth function $f(x)$ at two points $x_1$ and $x_2$ which are close to each other. The magnitude of the expected result, $|\...
0
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28 views

Obtaining integer digits using the GNU Multiprecision Arithmetic Library (gmplib)

I'm using the GNU Multiprecision Arithmetic Library (gmplib) for some experiments in computational mathematics. I want to extract, and manipulate, the base-b digits (with 2 <= b <= 10) of ...