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.

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5
votes
2answers
118 views

Odd accuracy barrier in C/PETSc regarding finite elements

I’m implementing a finite element code (translating from a working MATLAB version, so I have results to compare to) and for some odd reason, some of my computations are only accurate to around 6 ...
2
votes
2answers
1k views

Determine the step size in a differential equation numerical solver

How can we define the precision we require in a numerical differential equation solver? What is it that I have to optimize to know? And how do I know that I'm at a sufficient time-step value? For ...
4
votes
1answer
5k views

Machine epsilon (eps)

The wiki for machine epsilon says: "Machine epsilon gives an upper bound on the relative error due to rounding in floating point arithmetic" If machine epsilon is the upper bound on the relative ...
1
vote
3answers
2k views

Matlab output in scientific notation [ERROR: Subscript indices must either be real positive integers or logicals.]

I have X, Y and Z variables in matrix form, each of size n x 1. Eg.: X = [-38.0400, -38.6700, -38.9300, -39.4500...] Whenever I run the code below: ...
14
votes
1answer
837 views

Scientific computing with Python with modern GPUs with double precision

Has anyone here used double precision scientific computing with new generation (e.g. K20) GPUs through Python? I know that this technology is rapidly evolving, but what is the best way to do this ...
7
votes
4answers
2k views

computing the determinant of a dense nonsymmetric 100x100 matrix having very big and very small eigenvalues

The motivation for my question is the following: in one of Project Euler questions there is a need to count the spanning trees of a rectangular grid graph of dimension 100x500. By the Matrix-Tree ...
6
votes
2answers
2k views

Need for quad precision in scientific computing?

Even if quad precision is not directly supported by most CPUs, many Compilers (GNU, Intel) support them. Also some software packages allow to compile with quad precision, e.g. PETSc. But is there ...
9
votes
2answers
716 views

Higher precision floating-point arithmetic in numerical PDE

I have the impression, from very different resources and talks with researches, that there is a growing demand for high precision computations in numerical partial differential equations. Here, high ...
10
votes
2answers
721 views

Diagonalization of Dense Ill Conditioned Matrices

I am trying to diagonalize some dense, ill-conditioned matrices. In machine precision, results are inaccurate (returning negative eigenvalues, eigenvectors do not have the expected symmetries). I ...
7
votes
5answers
569 views

What algorithm for solving a set of stiff ODEs would be easiest to port to high precision floating point arithmetic?

I want to solve a relatively small system of stiff ODEs (< 10 first-order equations) using high precision floating point arithmetic (using MPFR or alike). What would be the easiest algorithm to ...
13
votes
3answers
4k views

Single versus double floating-point precision

Single precision floating point numbers take up half the memory and on modern machines (even on GPUs it seems) operations can be done with them at almost twice the speed compared to double precision. ...
25
votes
6answers
4k views

How can the gravitational n-body problem be solved in parallel?

How can the gravitational n-body problem be solved numerically in parallel? Is precision-complexity tradeoff possible? How does precision influence the quality of the model?
23
votes
3answers
3k views

What's the state-of-the-art in highly oscillatory integral computation?

What's the state-of-the-art in the approximation of highly oscillatory integrals in both one dimension and higher dimensions to arbitrary precision?
7
votes
3answers
454 views

Does there exist an arbitrary-precision convex optimization solver?

I have a relatively simple convex optimization problem that involves less than 100 variables but contains a terribly ill-conditioned matrix. I have tried CVX and CPLEX; even though both can typically ...