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Questions tagged [accuracy]

For questions about characterizing or improving the accuracy of a computational method.

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13 votes
2 answers
8k views

Which Runge-Kutta method is more accurate: Dormand-Prince or Cash-Karp?

I simply want to know whether the Dormand-Prince Numerical Method or the Cash-Karp Numerical Method is more accurate.
ABBC's user avatar
  • 233
20 votes
2 answers
3k views

Practical example of why it is not good to invert a matrix

I am aware about that inverting a matrix to solve a linear system is not a good idea, since it is not as accurate and as efficient as directly solving the system or using LU, Cholesky or QR ...
Manu's user avatar
  • 459
25 votes
5 answers
795 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 ...
Daniel Trebbien's user avatar
6 votes
3 answers
183 views

Accurate evaluation of the sign of a polynomial

Let $p$ be a polynomial with floating-point coefficients and let $a$ be a floating-point value. Is there a method for accurately evaluating the sign of $p(a)$ in floating-point arithmetic? I don't ...
lhf's user avatar
  • 966
6 votes
1 answer
291 views

Whittaker-Shannon interpolation: Accuracy dies with speedup; can it be fixed?

With a truncated Whitaker-Shannon series (cardinal series) $$ f(t) = \sum_{j = 0}^{n-1} y_{j} \frac{\sin\left(\pi( \frac{t-t_0}{h} -j)\right)}{\pi\left(\frac{t-t_0}{h}-j\right)} $$ we can naively ...
user14717's user avatar
  • 2,155
3 votes
1 answer
6k views

Why a finite difference scheme would give second order of accuracy in norm L2 but 1.5 with L1 (while 1 with Linf)?

My finite difference scheme for the 2D Euler equations is second order accurate in theory, since all the terms are second order accurate, with the advective terms being third order. So I expect a rate ...
Millemila's user avatar
  • 435
10 votes
2 answers
2k 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 ...
Geoffrey Irving's user avatar
8 votes
1 answer
683 views

Accurate and efficient computation of the inverse Langevin function

The Langevin function $\mathcal{L}(x) = \mathrm{coth}(x) - \frac{1}{x}$ occurs in computations related to elastomers and paramagnetic materials. It is easily computed accurately and with high ...
njuffa's user avatar
  • 1,865
4 votes
2 answers
405 views

Intervals where the sign of a polynomial can be computed reliably

This is a follow-up of a previous question. Let $p$ be a polynomial with floating-point coefficients. Is there a method for finding intervals where evaluating $p$ in floating-point arithmetic always ...
lhf's user avatar
  • 966
2 votes
1 answer
142 views

Accuracy gap for apparently stable solution

I was reasoning about the behaviour of the methods I'm using for my simulation and I noticed that, considering $h_s$ as the timestep over which I have unstable solutions and $h_a$ as the timestep ...
Zebx's user avatar
  • 101
2 votes
2 answers
568 views

Precision loss in Matrix-Vector product when applying Finite-Difference scheme

I am applying a 6th order Finite-Difference differentiation scheme as seen in http://www.scholarpedia.org/article/Method_of_lines/example_implementation/dss006 There seems to be severe numerical/...
Dr Krishnakumar Gopalakrishnan's user avatar
2 votes
1 answer
7k views

Correct way of computing norm $L_2$ for a finite difference scheme

I am computing the rate of convergence of my finite difference scheme in norm $L_2$. Which is the correct way to compute it? This: \begin{align} L_2 &= \frac{1}{N}\sqrt{\sum_{j=1}^N(u^{...
Millemila's user avatar
  • 435