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Error bounds for the truncated Baker--Campbell--Hausdorff and Zassenhaus formulas in unitary problems
A. Arnal, F. Casas, J. L. Ruiz-Benito
The Baker--Campbell--Hausdorff (BCH) formula plays a critical role in many branches of mathematics and physics. It expresses the logarithm of the product of exponentials of non-com…
A note on the Baker--Campbell--Hausdorff series in terms of right-nested commutators
Ana Arnal, Fernando Casas, Cristina Chiralt
We get compact expressions for the Baker--Campbell--Hausdorff series $Z = \log(\e^X \, \e^Y)$ in terms of right-nested commutators. The reduction in the number of terms originates…
Continuous changes of variables and the Magnus expansion
Fernando Casas, Philippe Chartier, Ander Murua
In this paper, we are concerned with a formulation of Magnus and Floquet-Magnus expansions for general nonlinear differential equations. To this aim, we introduce suitable continuo…
A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators
Ana Arnal, Fernando Casas, Cristina Chiralt
We present a general expression for any term of the Magnus series as an iterated integral of a linear combination of independent right-nested commutators with given coefficients. T…
A note on trigonometric identities involving non-commuting matrices
Ana Arnal, Fernando Casas, Cristina Chiralt
An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutator…
Efficient computation of the Zassenhaus formula
Fernando Casas, Ander Murua, Mladen Nadinic
A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independ…