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Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory.
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Über die Quantenmechanik der Electronen in Kristallgittern
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Double Stern–Gerlach experiment and related collision phenomena
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Evaluation of the coefficients of the Campbell–Hausdorff formula
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The radiation theorem of Tomonaga, Swinger and Feynman
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An operator calculus having applications in Quantum Electrodynamics
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K.O. Friedrichs · 1953
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Algebraic aspects in the theory of systems of linear differential equations
W. Magnus · 1953
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On the exponential solution of differential equations for a linear operator
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Theory of Ordinary Differential Equations
E.A. Coddington and N. Levinson · 1955
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Continuous Markov processes and stochastic equations
G. Maruyama · 1955
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Ordinary Differential Equations
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Integration of paths, geometric invariants and a generalized Baker–Hausdorff formula
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L’application exponentielle dans les groupes de Lie résolubles
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Sur certain groupes de Lie résolubles, I; II
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Linear Operators. Part I: General Theory
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Résolution de l’equation matricielle U ˙ = p U \dot{U}=p{U} par produit infini d’exponentielles matricielles
F. Fer · 1958
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The Theory of Matrices
F.R. Gantmacher · 1959
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Introduction to Matrix Analysis
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The Baker–Hausdorff formula and a problem in Crystal Physics
G.H. Weiss and A.A. Maradudin · 1962
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Controllability of linear dynamical systems
R.E. Kalman, Y.-C. Ho, and K.S. Narendra · 1963
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Multiple Coulomb excitations of deformed nuclei
D.W. Robinson · 1963
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Note on global validity of the Baker–Hausdorff and Magnus theorems
J. Wei · 1963
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Lie algebraic solution of linear differential equations
J. Wei and E. Norman · 1963
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Generalized adiabatic invariance
L.M. Garrido · 1964
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On global representations of the solutions of linear differential equations as a product of exponentials
J. Wei and E. Norman · 1964
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Handbook of Mathematical Functions
M. Abramowitz and I.A. Stegun · 1965
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On expanding the exponential
K. Kumar · 1965
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On the exponential form of time-displacement operators in quantum mechanics
P. Pechukas and J.C. Light · 1966
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Exponential operators and parameter differentiation in quantum physics
R.M. Wilcox · 1967
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Inelastic molecular collisions: exponential solution of coupled equations for vibration-translation energy transfer
S.-K. Chan, J.C. Light, and J.-L. Lin · 1968
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On some applications of Magnus expansion in Nuclear Magnetic Resonance
W. Evans · 1968
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Coherent averaging effects in Magnetic resonance
U. Haeberlen and J.S. Waugh · 1968
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Linear Differential Operators, Part I
M.A. Naimark · 1968
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Canonical transformation governing temporal development in classical mechanics
S. Tani · 1968
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Explicit solution of the continuous Baker–Campbell–Hausdorff problem and a new expression for the phase operator
I. Bialynicki-Birula, B. Mielnik, and J. Plebański · 1969
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Exponential solution of the Schrödinger equation: potential scattering
D. Chang and J.C. Light · 1969
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High-order time-dependent perturbation theory for classical mechanics and for other systems of first-order ordinary differential equations
R.A. Marcus · 1970
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Combinatorial approach to Baker–Campbell–Hausdorff exponents
B. Mielnik and J. Plebański · 1970
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A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods
J.G.F. Belinfante and B. Kolman · 1972
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Riccati Differential Equations
W.T. Reid · 1972
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On exponential approximations for the evolution operator
D. Voslamber · 1972
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A theoretical study of fast proton-atomic hydrogen scattering
D. Baye and P.H. Heenen · 1973
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Rotational spectral line broadening of OCS by noble gases
W.A. Cady · 1974
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Linear Differential Equations with Periodic Coefficients
V.A. Yakubovich and V.M. Starzhinskii · 1975
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Magnus approximation for K-shell ionization by heavy-ion impact
J. Eichler · 1977
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Infinite products and T products of exponentials
M.V. Karasev and M.V. Mosolova · 1977
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Automatic solution of the Sturm–Liouville problem
P.B. Bailey, M.K. Gordon, and L.F. Shampine · 1978
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Nineteen dubious ways to compute the exponential of a matrix
C. B. Moler and C. F. Van Loan · 1978
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Chronological algebras and nonstationary vector fields
A.A. Agrachev and R.V. Gamkrelidze · 1979
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The exponential representation of flows and the chronological calculus
A.A. Agrachev and R.V. Gamkrelidze · 1979
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Exponential representation of solutions of ordinary differential equations
R.V. Gamkrelidze · 1979
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Algebraic aspects of perturbation theories
F. Spirig · 1979
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Ordinary Differential Equations
J.K. Hale · 1980
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Magnus expansion generator
D.P. Burum · 1981
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Fonctionnelles causales non linéaires et indéterminées non commutatives
M. Fliess · 1981
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Application of the Magnus expansion for high-order multiphoton excitation
I. Schek, J. Jortner, and M.L. Sage · 1981
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Magnus expansion for rotationally induced inner-shell excitation
U. Wille · 1981
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Infrared dynamics of QED and the asymptotic behavior of the electron form factor
H. D. Dahmen, B. Scholz, and F. Steiner · 1982
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Theory of broadband spin decoupling
J.S. Waugh · 1982
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Study, extension, and application of Floquet theory for quantum molecular systems in an oscillating field
K.F. Milfeld and R.E. Wyatt · 1983
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Quantal phase factors accompanying adiabatic changes
M.V. Berry · 1984
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An accurate and efficient scheme for propagating the time dependent Schrödinger equation
H. Tal-Ezer and R. Kosloff · 1984
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A high order method for the solution of the single channel Schrödinger equation
P.L. Devries · 1985
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Matrix Analysis
R.A. Horn and C.R. Johnson · 1985
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Dipole Magnus approximation for electron-atom collisions: Excitation of the resonance transitions of Li, Na and K
H.A. Hyman · 1985
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Numerical integration of the differential Riccati equation
C.S. Kenney and R.B. Leipnik · 1985
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Graphical rules for functions of the time-evolution operator
H. D. Dahmen, W. Krzyzanowski, and M.L. Larsen · 1986
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Principles of NMR in one and two Dimensions
R. R. Ernst, G. Bodenhausen, and A. Wokaun · 1986
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Unitary quantum time evolution by iterative lanczos reduction
T.J. Park and J.C. Light · 1986
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Mechanisms of inner-shell vacancy production in slow ion-atom collisions
U. Wille and R. Hippler · 1986
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Quantum phase corrections from adiabatic iteration
M.V. Berry · 1987
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The Numerical Analysis of Ordinary Differential Equations
J.C. Butcher · 1987
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New criterion for convergence of exponential perturbation theory in the Schrödinger representation
W.R. Salzman · 1987
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The Campbell–Baker–Hausdorff–Dynkin formula and solutions of differential equations
R. S. Strichartz · 1987
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Practical application of the unitary approximation to infrared singularities
H. D. Dahmen, T. Mannel, and P. Manakos · 1988
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An algebraic view to the operatorial ordering and its applications to Optics
G. Dattoli, J.C. Gallardo, and A. Torre · 1988
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A Riccati transformation method for solving linear BVP I: Theoretical aspects, II: Computational aspects
L. Dieci, M.R. Osborne, and R.D. Russell · 1988
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A resolution method for Riccati differential systems coupled in their quadratic terms
L. Jódar and H. Abou-Kandil · 1988
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Mathematical Methods of Classical Mechanics
V. I. Arnold · 1989
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Analytic properties for the Magnus operator for two solvable hamiltonians
S. Klarsfeld and J.A. Oteo · 1989
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Exponential infinite-product representations of the time displacement operator
S. Klarsfeld and J.A. Oteo · 1989
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Recursive generation of higher-order terms in the Magnus expansion
S. Klarsfeld and J.A. Oteo · 1989
From time-ordered products to Magnus expansion
J. A. Oteo and J. Ros · 2000
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Splitting methods for non-autonomous Hamiltonian equations
S. Blanes and P.C. Moan · 2001
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Floquet theory: exponential perturbative treatment
F. Casas, J. A. Oteo, and J. Ros · 2001
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Methods for the approximation of the matrix exponential in a Lie-algebraic setting
E. Celledoni and A. Iserles · 2001
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Renormalization in quantum field theory and the Riemann–Hilbert problem II. The β \beta -function, diffeomorphisms and the renormalization group
A. Connes and D. Kreimer · 2001
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Applied Analysis
J.K. Hunter and B. Nachtergaele · 2001
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The projected gradient method for least squares matrix approximations with spectral constraints
M.T. Chu and K.R. Driessel · 1990
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Magnus expansion and the two-neutrino oscillations in matter
J. C. D’Olivo and J.A. Oteo · 1990
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Quantum Mechanics
A. Galindo and P. Pascual · 1990
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Unpublished notes, 1990
B.S. Mityagin · 1990
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The Riccati Equation
S. Bittanti, A.J. Laub, and J.C. Willems, editors · 1991
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Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
R. Brockett · 1991
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A Magnus expansion for the equation Y ′ = A Y − Y B {Y}^{\prime}={AY}-{YB}
A. Iserles · 2001
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A. Iserles · 2001
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Time symmetry and high-order Magnus methods
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Quadrature methods based on the Cayley transform
A. Marthinsen and B. Owren · 2001
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A Lie algebraic approach to numerical integration of stochastic differential equations
T. Misawa · 2001
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Convergence of the exponential Lie series
P.C. Moan and J.A. Oteo · 2001
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Generalized polar decompositions on Lie groups with involutive automorphisms
H. Munthe-Kaas, R.G.W. Quispel, and A. Zanna · 2001
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Quantum field theory without infinities
E.V. Stefanovich · 2001
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Lie algebras associated with the exponential solutions of nonautonomous linear differential equations
R. Suárez and L. Sáenz · 2001
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The Fer expansion and time symmetry: a Strang-type approach
A. Zanna · 2001
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Generalized polar decompositions for the approximation of the matrix exponential
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High order optimized geometric integrators for linear differential equations
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