author = {M. Caliari and F. Zivcovich},

title = {On-the-fly backward error estimate for matrix exponential approximation by {T}aylor algorithm},

year = {2018},

journal = {J. Comput. Appl. Math.},

note = {Accepted for publication}

}

@article{CKZ18,

author = {M. Caliari and P. Kandolf and F. Zivcovich},

title = {Backward error analysis of polynomial approximations for computing the action of the matrix exponential},

year = {2018},

journal = {BIT},

note = {Accepted for publication}

}

@article{CZ18,

author = {M. Caliari and S. Zuccher},

title = {Reliability of the time splitting {F}ourier method for singular solutions in quantum fluids},

journal = {Comput. Phys. Commun.},

year = {2018},

volume = {222},

pages = {46--58}

}

@article{CZ172,

author = {M. Caliari and S. Zuccher},

title = {{INFFTM}: {F}ast evaluation of 3d {F}ourier series in {MATLAB} with an application to quantum vortex reconnection},

journal = {Comput. Phys. Commun.},

year = {2017},

volume = {213},

pages = {197--207}

}

@article{COP17,

author = {M. Caliari and A. Ostermann and C. Piazzola},

journal = {J. Comput. Appl. Math.},

title = {A splitting approach for the magnetic {S}chr\"odinger equation},

year = {2017},

volume = {316},

pages = {74--85}

}

@ARTICLE{CZ17,

author = {M. Caliari and S. Zuccher},

title = {Quasi-{N}ewton minimization for the $p(x)$-{L}aplacian problem},

journal = {J. Comput. Appl. Math.},

volume = {309},

pages = {122--131},

year = {2017}

}

@ARTICLE{CKOR16,

author = {M. Caliari and P. Kandolf and A. Ostermann and S. Rainer},

title = {The {L}eja method revisited: {B}ackward error analysis for the matrix exponential},

year = {2016},

journal = {SIAM J. Sci. Comput.},

volume = {38},

number = {3},

pages = {A1639--A1661}

}

@article{BC15,

author = {Bos, L. P. and M. Caliari},

journal = {Dolomites Res. Notes Approx.},

pages = {66--74},

title = {Application of modified {L}eja sequences to polynomial interpolation},

volume = {8},

year = {2015},

}

@ARTICLE{ZCBB12,

author = {S. Zuccher and M. Caliari and Baggaley, A. W. and Barenghi, C. F.},

title = {Quantum vortex reconnections},

year = 2012,

journal = {Phys. Fluids},

volume = {24},

issue = {12},

number = {125108},

}

@ARTICLE{CS12,

author = {M. Caliari and M. Squassina},

title = {On a bifurcation value related to quasi-linear {S}chr\"odinger equations},

year = {2012},

journal = {J. Fix. Point Theory Appl.},

volume = {12},

number = {1--2},

pages = {121--133}

}

@ARTICLE{COR11,

author = {M. Caliari and A. Ostermann and S. Rainer},

title = {Meshfree integrators},

year = 2011,

journal = {Oberwolfach Reports},

volume = 8,

number = 1,

pages = {883--885}

}

@ARTICLE{COR13S,

author = {M. Caliari and A. Ostermann and S. Rainer},

title = {Meshfree exponential integrators},

year = 2013,

journal = {SIAM J. Sci. Comput.},

volume = 35,

number = 1,

pages = {A431--A452}

}

@INPROCEEDINGS{COR13,

author = {M. Caliari and A. Ostermann and S. Rainer},

title = {A {M}eshfree splitting method for soliton dynamics in nonlinear {S}chr\"odinger equations},

journal = {Lect. Notes Comput. Sci. Eng.},

year = 2013,

booktitle = {Meshfree Methods for Partial Differential Equations VI},

series = {Lect. Notes Comput. Sci. Eng.},

editor = {M. Griebel and M. A. Schweitzer},

volume = 89,

publisher = {Springer},

pages = {127--139}

}

@ARTICLE{CS10,

author = {M. Caliari and M. Squassina},

title = {Numerical computation of soliton dynamics for {NLS} equations in a driving potential},

journal = {Electron. J. Diff. Eqns.},

volume = 89,

pages = {1--12},

year = 2010

}

@ARTICLE{CDMSV11,

author = {M. Caliari and De Marchi, S. and A. Sommariva and M. Vianello},

title = {{Padua2DM}: fast interpolation and cubature at the {P}adua points in {M}atlab/{O}ctave},

journal = {Numer. Algorithms},

volume = 56,

number = 1,

pages = {45--60},

year = 2011

}

@ARTICLE{BCV03,

author = {L. Bergamaschi and M. Caliari and M. Vianello},

title = {Efficient approximation of the exponential operator for discrete {2D} advection-diffusion problems},

journal = {Numer. Linear Algebra Appl.},

volume = 10,

number = 3,

pages = {271--289},

year = 2003

}

@ARTICLE{CVB04,

author = {M. Caliari and M. Vianello and L. Bergamaschi},

title = {Interpolating discrete advection-diffusion propagators at {L}eja sequences},

journal = {J. Comput. Appl. Math.},

volume = 172,

number = 1,

pages = {79--99},

year = 2004

}

@INPROCEEDINGS{BCV04,

author = {L. Bergamaschi and M. Caliari and M. Vianello},

title = {The {ReLPM} exponential integrator for {FE} discretizations of advection-diffusion equations},

booktitle = {Computational Science --- ICCS 2004},

series = {Lecture Notes in Comput. Sci.},

volume = 3039,

editor = {Bubak, M. and Albada, G. D. v. and Sloot, P. M. A. and J. Dongarra},

pages = {434--442},

note = {4th International Conference, Krak\'ow, Poland, June 6--9, 2004, Proceedings, Part IV},

publisher = {Springer},

address = {Berlin/Heidelberg},

year = 2004

} 5~5~

@ARTICLE{CIM04,

author = {M. Caliari and G. Inverso and Morato, L. M.},

title = {Dissipation caused by a vorticity field and generation of singularities in {M}adelung fluid},

journal = {New J. Phys.},

volume = 6,

number = 69,

year = 2004

}

@ARTICLE{CDMV05,

author = {M. Caliari and De Marchi, S. and M. Vianello},

title = {Bivariate polynomial interpolation on the square at new nodal sets},

journal = {Appl. Math. Comput.},

volume = 165,

number = 2,

pages = {261--274},

year = 2005

}

@INPROCEEDINGS{BCMV05,

author = {L. Bergamaschi and M. Caliari and A. Mart\'\i{}nez and M. Vianello},

title = {A parallel exponential integrator for large-scale discretizations of advection-diffusion models},

booktitle = {Recent Advances in Parallel Virtual Machine and Message Passing Interface},

series = {Lecture Notes in Comput. Sci.},

volume = 3666,

editor = {Di Martino, B. and D. Kranzlm\"uller and J. Dongarra},

pages = {483--492},

note = {12th European PVM/MPI Users' Group Meeting Sorrento, Italy, September 18--21, 2005. Proceedings},

publisher = {Springer},

address = {Berlin/Heidelberg},

year = 2005

}

@INPROCEEDINGS{BCMV06,

author = {L. Bergamaschi and M. Caliari and A. Mart\'\i{}nez and M. Vianello},

title = {Comparing {L}eja and {K}rylov approximations of large scale matrix exponentials},

booktitle = {Computational Science --- ICCS 2006},

series = {Lecture Notes in Comput. Sci.},

note = {6th International Conference, Reading, UK, May 28--31, 2006, Proceedings, Part IV},

volume = 3994,

editor = {Alexandrov, V. N. and van Albada, G. D. and Sloot, P. M. A. and J. Dongarra},

pages = {685--692},

publisher = {Springer},

address = {Berlin/Heidelberg},

year = 2006

}

@ARTICLE{BCDMV06C,

author = {L. Bos and M. Caliari and De Marchi, S. and M. Vianello},

title = {A numerical study of the {X}u interpolation formula in two variables},

journal = {Computing},

volume = 76,

number = {3--4},

pages = {311--324},

year = 2006

}

@ARTICLE{BCDMV06E,

author = {L. Bos and M. Caliari and De Marchi, S. and M. Vianello},

title = {Bivariate interpolation at {X}u points: results, extensions and applications},

journal = {Electron. Trans. Numer. Anal.},

volume = 25,

pages = {1--16},

year = 2006

}

@ARTICLE{CVB07,

author = {M. Caliari and M. Vianello and L. Bergamaschi},

title = {The {LEM} exponential integrator for advection-diffusion-reaction equations},

journal = {J. Comput. Appl. Math.},

note = {Proc. of Numerical Analysis: the State of the Art (NAC2005), Rende (CS), Italy, May 19--21, 2005},

volume = 210,

number = {1--2},

pages = {56--63},

year = 2007

}

@ARTICLE{BCDMVX06,

author = {L. Bos and M. Caliari and De Marchi, S. and M. Vianello and Y. Xu},

title = {Bivariate {L}agrange interpolation at the {P}adua points: the generating curve approach},

journal = {J. Approx. Theory},

volume = 143,

number = 1,

pages = {15--25},

year = 2006

}

@ARTICLE{CVDMM06,

author = {M. Caliari and M. Vianello and De Marchi, S. and R. Montagna},

title = {{HYPER2D}: a numerical code for hyperinterpolation at {X}u points on rectangles},

journal = {Appl. Math. Comp.},

volume = 183,

number = 2,

pages = {1138--1147},

year = 2006

}

@ARTICLE{CDMV07,

author = {M. Caliari and De Marchi, S. and M. Vianello},

title = {Hyperinterpolation on the square},

journal = {J. Comput. Appl. Math.},

note = {Proc. of Numerical Analysis: the State of the Art (NAC2005), Rende (CS), Italy, May 19--21, 2005},

volume = 210,

number = {1--2},

pages = {78--83},

year = 2007

}

@ARTICLE{C07,

author = {M. Caliari},

title = {Accurate evaluation of divided differences for polynomial interpolation of exponential propagators},

journal = {Computing},

volume = 80,

number = 2,

pages = {189--201},

year = 2007

}

@ARTICLE{MBCV09,

author = {A. Mart\'\i{}nez and L. Bergamaschi and M. Caliari and M. Vianello},

title = {A massively parallel exponential integrator for advection-diffusion models},

journal = {J. Comput. Appl. Math.},

volume = 231,

number = 1,

pages = {82--91},

year = 2009

}

@ARTICLE{CVDM08,

author = {M. Caliari and De Marchi, S. and M. Vianello},

title = {Algorithm 886: {Padua2D}: {L}agrange {I}nterpolation at {P}adua {P}oints on {B}ivariate {D}omains},

journal = {ACM Trans. Math. Software},

volume = 35,

number = 3,

pages = {21:1--21:11},

year = 2008

}

@ARTICLE{CDMV08JCAM,

author = {M. Caliari and De Marchi, S. and M. Vianello},

title = {Bivariate {L}agrange interpolation at the {P}adua points: {C}omputational aspects},

journal = {J. Comput. Appl. Math.},

volume = 221,

number = 2,

pages = {284--292},

year = 2008

}

@ARTICLE{CDMV08,

author = {M. Caliari and De Marchi, S. and M. Vianello},

title = {Hyperinterpolation in the cube},

journal = {Comp. Math. Appl.},

volume = 55,

number = 11,

pages = {2490--2497},

year = 2008

}

@ARTICLE{CO09,

author = {M. Caliari and A. Ostermann},

title = {Implementation of exponential {R}osen\-brock-type methods},

journal = {Appl. Numer. Math.},

volume = 59,

number = {3--4},

pages = {568--581},

year = 2009

}

@MISC{CO07B,

author = {M. Caliari and A. Ostermann},

title = {Exponential integrators for linear advection and wave equations},

note = {in preparation},

year = 2007

}

@ARTICLE{CS08,

author = {M. Caliari and M. Squassina},

title = {Location and phase segregation of ground and excited states for {2D} {G}ross--{P}itaevskii systems},

journal = {Dyn. Partial Differ. Equ.},

pages = {117--137},

volume = 5,

number = 2,

year = 2008

}

@ARTICLE{CS082,

author = {M. Caliari and M. Squassina},

title = {Spatial patterns for the three species {G}ross--{P}itaevskii system in the plane},

journal = {Electron. J. Diff. Eqns.},

volume = 2008,

number = 79,

pages = {1--15},

year = 2008

}

@MISC{CKT07,

author = {M. Caliari and G. Kirchner and M. Thalhammer},

title = {Convergence and energy conservation of the {S}trang time-splitting {H}ermite spectral method for nonlinear {S}chr\"odinger equations},

note = {submitted},

year = 2007

}

@ARTICLE{CORT09,

author = {M. Caliari and A. Ostermann and S. Rainer and M. Thalhammer},

title = {A minimisation approach for computing the ground state of {G}ross--{P}itaevskii systems},

journal = {J. Comput. Phys.},

volume = 228,

number = 2,

pages = {349--360},

year = 2009

}

@ARTICLE{CNT09,

author = {M. Thalhammer and M. Caliari and Ch. Neuhauser},

title = {High-order time-splitting {H}ermite and {F}ourier spectral methods for the {G}ross--{P}itaevskii equation},

journal = {J. Comput. Phys.},

volume = 228,

number = 3,

pages = {822--832},

year = 2009

}

@ARTICLE{CLMZ08,

author = {M. Caliari and Loffredo, M. I. and Morato, L. M. and S. Zuccher},

title = {Cubic Nonlinear {S}chr\"odinger Equation with vorticity},

journal = {New J. Phys.},

volume = 10,

number = 123020,

year = 2008

}

@ARTICLE{CR13,

author = {M. Caliari and S. Rainer},

title = {{GSGPEs}: a {MATLAB} code for computing the ground state of systems of {G}ross--{P}itaevskii equations},

journal = {Comput. Phys. Commun.},

volume = 184,

number = 3,

pages = {812--823},

year = {2013}

}

@ARTICLE{BCS13,

author = {M. Bellomi and M. Caliari and M. Squassina},

title = {Computing the first eigenpar for problems with variable exponents},

year = {2013},

journal = {J. Fix. Point Theory Appl.},

volume = {13},

number = {2},

pages = {561--570}

}

@ARTICLE{CKOR14,

author = {M. Caliari and P. Kandolf and A. Ostermann and S. Rainer},

title = {Comparison of software for computing the action of the matrix exponential},

year = {2014},

journal = {BIT},

volume = 54,

number = 1,

pages = {113--128},

doi = {10.1007/s10543-013-0446-0}

}

@ARTICLE{AZCPPB14,

author = {Allen, A. J. and S. Zuccher and M. Caliari and Proukakis, N. P. and Parker, N. G. and Barenghi, C. F. },

title = {Vortex reconnections in atomic condensates at finite temperature},

journal = {Phys. Rev. A},

volume = {90},

pages = {013601},

year = {2014}

}

@ARTICLE{CZ15,

author = {M. Caliari and S. Zuccher},

title = {The inverse power method for the $p(x)$-{L}aplacian problem},

journal = {J. Sci. Comput.},

volume = {65},

number = {2},

pages = {698--714},

year = {2015} }