Rational Krylov Toolbox for MATLAB  Download    Guide   Examples





The RKToolbox is a collection of scientific computing tools
based on rational Krylov techniques.


Welcome to the RKToolbox
This plot visualizes the convergence of rational Ritz values for a symmetric matrix.
Hold on to see some slides with use cases of the RKToolbox.
Solve large-scale linear and nonlinear eigenvalue problems: Solve large-scale linear and nonlinear eigenvalue problems
AB  = util_linearise_nlep(A, Sigma, Xi, tol, Nmax);
[V, K, H] = rat_krylov(AB, v, shifts);
Design rational filters using numerical arithmetic operations: Design rational filters using numerical arithmetic operations
x = rkfun; f1 = rkfun('step',5); f2 = rkfun('cheby',3);
f2 = 1./(1 + 0.05*f2(2*x-2).^2); ezplot(f1+f2)
Partial fraction conversion and root-finding for rational functions: Partial fraction conversion and root-finding for rational functions
r = rkfun('(x^3 - x^2 + 1)/(x^4 + 1)'); s = rkfun('cayley');
res = residue(r(s)); rts = roots(r(s)); pls = poles(r(s));
Nonlinear fitting of transfer functions and pole identification: Nonlinear fitting of transfer functions and pole identification
This slide shows the fitting of a frequency response using the RKFIT algorithm.
See this example for more details.
Parameter optimization for matrix function approximation: Parameter optimization for matrix function approximation
Optimized poles for the approximation of the matrix exponential function.
See this example for more details.

The RKToolbox is downloaded and installed within seconds:

The RKToolbox is downloaded and installed within seconds

To get started, have a look at the guide and example collection.

Please contact us with any feedback or questions:

Mario      Steven     Stefan
Mario Berljafa            Steven Elsworth            Stefan Güttel


The University of Manchester