The results can never be worse than ordinary interval arithmetic. Note, however, that it is not sufficient to solve the four extreme cases because the dependence is nonlinear. Some random entry of the input matrix is replaced by an interval, all other entries of the matrix and the right hand side are single floating-point numbers. Opportunities for recent engineering grads. For details see the affari demo. Obviously, the computed inclusion Y is a true inclusion of the range, but an overestimation. Rump at Hamburg University of Technology, Germany.

intlab matlab

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For example, finding the global minimum of the Griewank may be tried by local methods, possibly evaluating the function on a very fine grid.

intlab matlab

INTLAB comprises of self-validating methods for dense linear systems intlav inner inclusions and structured matrices sparse s. The fl-toolbox An example of interval overestimation: Cancel Copy to Clipboard.

intlab matlab

Sometimes it is interesting to know the result of a computation using some limited precision. The green line is the convex hull of the Bernstein coefficients.

intlab matlab

All roots of a system of nonlinear equations verified global optimization verified constraint global optimization parameter identification roots of univariate and multivariate nonlinear equations simple and clusters eigenvalue problems simple and clusters, also inner inclusions and structured matrices generalized eigenvalue problems simple and clusters quadrature for univariate functions univariate polynomial zeros simple and clusters forward and backward FFT interval arithmetic for real and complex data including vectors and matrices very fast interval arithmetic for real and complex sparse matrices very fast affine arithmetic including vectors and matrices gradients using affine arithmetic Hessians using affine arithmetic Taylor expansion using affine arithmetic fl-numbers: The large red box is the result by ordinary interval arithmetic, the blue parallel-epiped inside the result by affine arithmetic.


Consider a randomly generated linear system with interval matrix A and right hand side b such that A. For a given linear system with data afflicted with tolerances one may want to compute the smallest box around the set of all solution for data varying within the tolerances.

INTLAB Version 9 for Matlab and Octave

Sometimes there is not much overestimation. However, intlaab inner inclusion decovers that this inclusion is not too far from the narrowest inclusion of the solution set. Here is a simple example.

Moreover, some routines treat extremely ill-conditioned problems. When solving a linear system with interval data, by default all data are assumed to vary independently within the tolerances. Intla random points suggest that the computed inclusion is quite an overestimation of the true range of the first two components. Further reading My page review paper Verification methods: However, nonlinear computations and loops may slow down the system significantly due to interpretation overhead intlsb extensive use of the operator concept.

INTLAB Version 9 for Matlab and Octave

Using only floating-point arithmetic that is particularly difficult if the global behaviour of a function is to be estimated. In this demo the graph is produced before-hand. Matab, if we repeat the plot with 50 meshpoints in x- and y-direction, then the function decovers its ugly behaviour. The overestimation is caused by the fact that the supporting hyperplanes of interval vectors are parallel to the axes. There may be some interval processing code in the Symbolic Toolbox. Zooming into the picture shows red and yellow areas.


We may try to estimate the range of the function over the whole domain by taking the minimum and maximum in the nodes. The following shows both the result using ordinary interval arithmetic and using affine arithmetic. However, there are many counterexamples to that. We defined a right hand side such that the true solution of the midpoint linear system is [1,-1,1,-1, Please consult “demo intval” [direct call web ‘dintval.

It runs under the forthcoming Matlab version Rb and is downward compatible at least to Rb.

INTLAB download for free,how? – MATLAB Answers – MATLAB Central

Details and examples are here. Select the China site in Chinese or English for best site performance. In our example this implies that the matrix depends only on two parameters. Reload the page to see its updated state.

Details and examples about timing can be found here. Consider the following linear system, the matrix arising from the classic second difference operator on n points. In particular the new ODE toolbox uses Matlab features which are not yet supported by Octave; we try to find workarounds.