The accuracy tag has no wiki summary.
3
votes
0answers
80 views
How to accurately decompose positive semidefinite matrix and use the lower triangular part in linear equations
I have $n$ arbitrary $p\times 1$ vectors $x_i$, and $p\times k$ matrices $A_i$, and $n$ $p \times p$ positive semidefinite matrices $S_i$, where some (often most) of the $S_i$'s are same (for example ...
7
votes
1answer
139 views
Are there Improved ways of computing $p \log(p)$?
Most math libraries have a number of versions of logarithm functions.
Most of the time we assume them to be perfect, but actually quite a lot of them just offer a certain number of digits of ...
5
votes
3answers
208 views
Fast and accurate double precision implementation of incomplete gamma function
What is the state of the art way of implementing double precision special functions? I need the following integral:
$$
F_m(t) = \int_0^1 u^{2m} e^{-tu^2} d u
= {\gamma(m+{1\over 2}, ...
6
votes
1answer
90 views
Demonstrating that the time step size is small enough in a code with automatic step size selection
I recently inherited a large body of legacy code that solves a very stiff, transient problem. I would like to demonstrate that the spatial and temporal step sizes are small enough that the ...
0
votes
0answers
55 views
Compare accuracy of two different measurement devices [closed]
I'm currently trying to compare the measurement accuracy of two devices. However, I am using one of the devices as a "gold standard" to say something about the accuracy of the other device.
The ...
9
votes
2answers
136 views
How do you improve the accuracy of a finite difference method for finding the eigensystem of a singular linear ODE
I am attempting to solve an equation of the type:
$ \left( -\tfrac{\partial^2}{\partial x^2} - f\left(x\right) \right) \psi(x) = \lambda \psi(x) $
Where $f(x)$ has a simple pole at $0$, for the ...
7
votes
2answers
330 views
Are 8 Gauss points required for second order hexahedral finite elements?
Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical ...
18
votes
5answers
450 views
Is there software that can autogenerate numerically-accurate floating point C routines from symbolic formulae?
Given a real function of real variables, is there software available that can automatically generate numerically-accurate code to calculate the function over all inputs on a machine equipped with IEEE ...
5
votes
2answers
271 views
numerical integration with possible division by 'zero'
I am trying to integrate
$$\int^1_0 t^{2n+2}\exp\left({\frac{\alpha r_0}{t}}\right)dt$$
which is a simple transformation of
$$\int^{\infty}_1 x^{2n}\exp(-\alpha r_0 x)dx$$
using $t = \frac1{x}$ ...
14
votes
3answers
275 views
When is a high order method useful for computational fluid dynamics simulations?
Many numerical approaches to CFD can be extended to arbitrarily high order (for instance, discontinuous Galerkin methods, WENO methods, spectral differencing, etc.). How should I choose an ...
