Polynomially scaling spin dynamics II: Further state-space compression using Krylov subspace techniques and zero track elimination

Journal of Magnetic Resonance

Volumn 195, Issue 1, 2008, Pages 45-51

  Kuprov, Ilya ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

EPR; NMR; Scaling; Simulation; Spin

Indexed keywords

COMPOSITE STRUCTURES; DYNAMICS; FEATURE EXTRACTION; LINGUISTICS; NUCLEAR MAGNETIC RESONANCE; QUANTUM THEORY; SEMICONDUCTOR RELAYS; STATE SPACE METHODS;

EPR; NMR; SCALING; SIMULATION; SPIN;

SPIN DYNAMICS;

ALGORITHM; ARTICLE; CHEMICAL MODEL; COMPUTER SIMULATION; INFORMATION PROCESSING; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; SPIN LABELING;

ALGORITHMS; COMPUTER SIMULATION; DATA COMPRESSION; MAGNETIC RESONANCE SPECTROSCOPY; MODELS, CHEMICAL; SPIN LABELS;

EID: 53549128361     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2008.08.008     Document Type: Article

References (31)

1. Bak M., Rasmussen J.T., and Nielsen N.C. SIMPSON: a general simulation program for solid-state NMR spectroscopy. J. Magn. Reson. 147 (2000) 296-330
2. Ernst R.R., Bodenhausen G., and Wokaun A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions (1987), Clarendon Press, Oxford
3. Hodgkinson P., and Emsley L. Numerical simulation of solid-state NMR experiments. Progr. NMR Spec. 36 (2000) 201-239
4. Mehring M., and Weberruss V.A. Object-oriented magnetic resonance: classes and objects, calculations and computations (2001), Academic Press, San Diego, California
5. Nielsen N.C. Computational aspects of biological solid-state NMR spectroscopy. In: Ramamoorthy A. (Ed). NMR Spectroscopy of Biological Solids (2006), CRC/ Taylor & Francis pp. 261-304
6. Sivertsen A.C., Bjerring M., Kehlet C.T., Vosegaard T., and Nielsen N.C. Numerical simulations in biological solid-state NMR spectroscopy. Annu. Rep. NMR Spectr. 54 (2005) 243-293
7. Smith S.A., Levante T.O., Meier B.H., and Ernst R.R. Computer simulations in magnetic resonance. An object-oriented programming approach. J. Magn. Reson. 106 (1994) 75-105
8. Veshtort M., and Griffin R.G. SPINEVOLUTION: a powerful tool for the simulation of solid and liquid state NMR experiments. J. Magn. Reson. 178 (2006) 248-282
9. Jerschow A. MathNMR: spin and spatial tensor manipulations in mathematica. J. Magn. Reson. 176 (2005) 7-14
10. Kuprov I., Wagner-Rundell N., and Hore P.J. Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software. J. Magn. Reson. 184 (2007) 196-206
11. Dumont R.S., Jain S., and Bain A. Simulation of many-spin system dynamics via sparse matrix methodology. J. Chem. Phys. 106 (1997) 5928-5936
12. Hodgkinson P., Sakellariou D., and Emsley L. Simulation of extended periodic systems of nuclear spins. Chem. Phys. Lett. 326 (2000) 515-522
13. Moro G., and Freed J.H. Calculation of ESR spectra and related Fokker-Planck forms by the use of the Lanczos algorithm. J. Chem. Phys. 74 (1981) 3757-3773
14. Doronin S.I., Fel'dman E.B., Kuznetsova E.I., Furman G.B., and Goren S.D. Dipolar temperature and multiple-quantum NMR dynamics in dipolar ordered-spin systems. JETP Lett. 86 (2007) 24-27
15. Doronin S.I., Fel'dman E.B., and Lacelle S. Multiple-quantum nuclear magnetic resonance spin dynamics in disordered rigid chains and rings. J. Chem. Phys. 117 (2002) 9646-9650
16. Fel'dman E.B., Bruschweiler R., and Ernst R.R. From regular to erratic quantum dynamics in long spin 1/2 chains with an XY Hamiltonian. Chem. Phys. Lett. 294 (1998) 297-304
17. Kuprov I., Wagner-Rundell N., and Hore P.J. Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction. J. Magn. Reson. 189 (2007) 241-250
18. Bai Z. Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl. Numer. Math. 43 (2002) 9-44
19. Freund R.W. Model reduction methods based on Krylov subspaces. Acta Numer. 12 (2003) 267-319
20. Vasavada K.V., Schneider D.J., and Freed J.H. Calculation of ESR spectra and related Fokker-Planck forms by the use of the Lanczos algorithm. II. Criteria for truncation of basis sets and recursive steps utilizing conjugate gradients. J. Chem. Phys. 86 (1986) 647-661
21. Nielsen N.C., and Sorensen O.W. Accessible states in Liouville space. A two-dimensional extension of the universal bound on spin dynamics applied to polarization transfer in INSM Spin- systems. J. Magn. Reson. 99 (1992) 449-465
22. Nielsen N.C., and Sorensen O.W. 2D bounds on polarization transfer involving quadrupolar spin nuclei. J. Magn. Reson. 99 (1992) 214-222
23. Van Beek J.D., Carravetta M., Antonioli G.C., and Levitt M.H. Spherical tensor analysis of nuclear magnetic resonance signals. J. Chem. Phys. 122 (2005) 1-12
24. Guntert P., Schaefer N., Otting G., and Wuthrich K. POMA: a complete mathematica implementation of the NMR product-operator formalism. J. Magn. Reson. A 101 (1993) 103-105
25. Moler C., and Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45 (2003) 3-49
26. Sidje R.B. Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Soft. 24 (1998) 130-156
27. Cahill E., Irving A., Johnston C., and Sexton J. Numerical stability of Lanczos methods. Nucl. Phys. B 83-84 (2000) 825-827
28. N.J. Higham, Accuracy and Stability of Numerical Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, 1996.
29. Gugercin S. An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems. Lin. Alg. Appl. 428 (2008) 1964-1986
30. Knyazev A.V. Preconditioned eigensolvers-An oxymoron?. Electr. Trans. Num. Anal. 7 (1998) 104-123
31. Hochbruck M., and Lubich C. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34 (1997) 1911-1925