{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T01:00:15Z","timestamp":1776474015278,"version":"3.51.2"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T00:00:00Z","timestamp":1487289600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004733","name":"University of Macau","doi-asserted-by":"crossref","award":["MYRG2016-00202-FST"],"award-info":[{"award-number":["MYRG2016-00202-FST"]}],"id":[{"id":"10.13039\/501100004733","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Science and Technology Development Fund, Macao S.A.R (FDCT)","award":["115\/2013\/A3"],"award-info":[{"award-number":["115\/2013\/A3"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2017,11]]},"DOI":"10.1007\/s11075-017-0272-6","type":"journal-article","created":{"date-parts":[[2017,2,16]],"date-time":"2017-02-16T22:35:26Z","timestamp":1487284526000},"page":"605-616","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["A fast numerical method for block lower triangular Toeplitz with dense Toeplitz blocks system with applications to time-space fractional diffusion equations"],"prefix":"10.1007","volume":"76","author":[{"given":"Yun-Chi","family":"Huang","sequence":"first","affiliation":[]},{"given":"Siu-Long","family":"Lei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,2,17]]},"reference":[{"issue":"6","key":"272_CR1","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1029\/2000WR900031","volume":"36","author":"DA Benson","year":"2000","unstructured":"Benson, D.A., Wheatcraft, S.W., Meerschaert, M.M.: Application of a fractional advection-dispersion equation. Water Resour. Res. 36(6), 1403\u20131412 (2000)","journal-title":"Water Resour. Res."},{"key":"272_CR2","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198527688.001.0001","volume-title":"Numerical Methods for Structured Markov Chains","author":"DA Bini","year":"2005","unstructured":"Bini, D.A., Latouche, G., Meini, B.: Numerical Methods for Structured Markov Chains. Oxford University Press, New York (2005)"},{"key":"272_CR3","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718850","volume-title":"An Introduction to Iterative Toeplitz Solvers, vol. 5","author":"R Chan","year":"2007","unstructured":"Chan, R., Jin, X.: An Introduction to Iterative Toeplitz Solvers, vol. 5. SIAM, Philadelphia (2007)"},{"issue":"3","key":"272_CR4","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1137\/s0036144594276474","volume":"38","author":"RH Chan","year":"1996","unstructured":"Chan, R.H., Ng, M.K.: Conjugate gradient methods for Toeplitz systems. SIAM Rev. 38(3), 427\u2013482 (1996). doi:\n                        10.1137\/s0036144594276474","journal-title":"SIAM Rev."},{"key":"272_CR5","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.apnum.2013.03.006","volume":"70","author":"M Chen","year":"2013","unstructured":"Chen, M., Deng, W., Wu, Y.: Superlinearly convergent algorithms for the two-dimensional space\u2013time Caputo\u2013Riesz fractional diffusion equation. Appl. Numer. Math. 70, 22\u201341 (2013). doi:\n                        10.1016\/j.apnum.2013.03.006","journal-title":"Appl. Numer. Math."},{"issue":"5","key":"272_CR6","doi-asserted-by":"publisher","first-page":"730","DOI":"10.1007\/bf01200697","volume":"15","author":"I Gohberg","year":"1992","unstructured":"Gohberg, I., Olshevsky, V.: Circulants, displacements and decompositions of matrices. Integr. Equat. Oper. Th. 15(5), 730\u2013743 (1992). doi:\n                        10.1007\/bf01200697","journal-title":"Integr. Equat. Oper. Th."},{"key":"272_CR7","doi-asserted-by":"crossref","DOI":"10.1142\/3779","volume-title":"Applications of Fractional Calculus in Physics","author":"R Hilfer","year":"2000","unstructured":"Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)"},{"key":"272_CR8","volume-title":"Preconditioning Techniques for Toeplitz Systems","author":"X Jin","year":"2010","unstructured":"Jin, X.: Preconditioning Techniques for Toeplitz Systems. Higher Education Press, Beijing (2010)"},{"key":"272_CR9","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.jcp.2015.09.042","volume":"303","author":"R Ke","year":"2015","unstructured":"Ke, R., Ng, M.K., Sun, H.: A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations. J. Comput. Phys. 303, 203\u2013211 (2015). doi:\n                        10.1016\/j.jcp.2015.09.042","journal-title":"J. Comput. Phys."},{"key":"272_CR10","doi-asserted-by":"publisher","unstructured":"Lei, S., Huang, Y.: Fast algorithms for high-order numerical methods for space fractional diffusion equations. Int. J. Comput. Math. (2016). doi:\n                        10.1080\/00207160.2016.1149579","DOI":"10.1080\/00207160.2016.1149579"},{"key":"272_CR11","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1016\/j.jcp.2013.02.025","volume":"242","author":"S Lei","year":"2013","unstructured":"Lei, S., Sun, H.: A circulant preconditioner for fractional diffusion equations. J. Comput. Phys. 242, 715\u2013725 (2013). doi:\n                        10.1016\/j.jcp.2013.02.025","journal-title":"J. Comput. Phys."},{"issue":"1","key":"272_CR12","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.amc.2006.08.162","volume":"191","author":"F Liu","year":"2007","unstructured":"Liu, F., Zhuang, P., Anh, V., Turner, I., Burrage, K.: Stability and convergence of the difference methods for the space\u2013time fractional advection\u2013diffusion equation. Appl. Math. Comput. 191(1), 12\u201320 (2007). doi:\n                        10.1016\/j.amc.2006.08.162","journal-title":"Appl. Math. Comput."},{"issue":"5","key":"272_CR13","doi-asserted-by":"publisher","first-page":"866","DOI":"10.1002\/nla.1972","volume":"22","author":"X Lu","year":"2015","unstructured":"Lu, X., Pang, H., Sun, H.: Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations. Numer. Linear Algebra Appl. 22(5), 866\u2013882 (2015). doi:\n                        10.1002\/nla.1972","journal-title":"Numer. Linear Algebra Appl."},{"key":"272_CR14","volume-title":"Fractional Calculus in Bioengineering","author":"RL Magin","year":"2006","unstructured":"Magin, R.L.: Fractional Calculus in Bioengineering. Danbury, Begell House Redding (2006)"},{"key":"272_CR15","volume-title":"Iterative Methods for Toeplitz Systems","author":"MK Ng","year":"2004","unstructured":"Ng, M.K.: Iterative Methods for Toeplitz Systems. Oxford University Press, New York (2004)"},{"key":"272_CR16","doi-asserted-by":"publisher","unstructured":"Pang, H., Sun, H.: Fourth order finite difference schemes for time\u2013space fractional sub-diffusion equations. Comput. Math. Appl. (2016). doi:\n                        10.1016\/j.camwa.2016.02.011","DOI":"10.1016\/j.camwa.2016.02.011"},{"key":"272_CR17","volume-title":"Fractional Differential Equations, vol. 198","author":"I Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations, vol. 198. Academic Press, New York (1999)"},{"issue":"1","key":"272_CR18","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1016\/S0378-4371(02)01048-8","volume":"314","author":"M Raberto","year":"2002","unstructured":"Raberto, M., Scalas, E., Mainardi, F.: Waiting-times and returns in high-frequency financial data: an empirical study. Physica. A 314(1), 749\u2013755 (2002). doi:\n                        10.1016\/S0378-4371(02)01048-8","journal-title":"Physica. A"},{"issue":"11","key":"272_CR19","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1103\/PhysRevLett.58.1100","volume":"58","author":"M Shlesinger","year":"1987","unstructured":"Shlesinger, M., West, B., Klafter, J.: L\u00e9vy dynamics of enhanced diffusion: application to turbulence. Phys. Rev. Lett. 58(11), 1100 (1987). doi:\n                        10.1103\/PhysRevLett.58.1100","journal-title":"Phys. Rev. Lett."},{"key":"272_CR20","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/j.amc.2016.01.044","volume":"281","author":"H Sun","year":"2016","unstructured":"Sun, H., Sun, Z., Gao, G.: Some high order difference schemes for the space and time fractional bloch\u2013torrey equations. Appl. Math. Comput. 281, 356\u2013380 (2016). doi:\n                        10.1016\/j.amc.2016.01.044","journal-title":"Appl. Math. Comput."},{"key":"272_CR21","volume-title":"Elliptic Problems in Linear Difference Equations over a Network. Watson Scientific Computing Laboratory Report","author":"L Thomas","year":"1949","unstructured":"Thomas, L.: Elliptic Problems in Linear Difference Equations over a Network. Watson Scientific Computing Laboratory Report. Columbia University Press, New York (1949)"},{"key":"272_CR22","doi-asserted-by":"publisher","unstructured":"Vong, S., Lyu, P., Chen, X., Lei, S.: High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives. Numer. Algor. (2015). doi:\n                        10.1007\/s11075-015-0041-3","DOI":"10.1007\/s11075-015-0041-3"},{"key":"272_CR23","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.cma.2014.01.026","volume":"273","author":"H Wang","year":"2014","unstructured":"Wang, H., Tian, H.: A fast and faithful collocation method with efficient matrix assembly for a two-dimensional nonlocal diffusion model. Comput. Methods in Appl. Mech. Eng. 273, 19\u201336 (2014). doi:\n                        10.1016\/j.cma.2014.01.026","journal-title":"Comput. Methods in Appl. Mech. Eng."},{"issue":"12","key":"272_CR24","doi-asserted-by":"publisher","first-page":"2596","DOI":"10.1080\/00207160.2015.1077948","volume":"92","author":"W Wang","year":"2015","unstructured":"Wang, W., Chen, X., Ding, D., Lei, S.: Circulant preconditioning technique for barrier options pricing under fractional diffusion models. Int. J. Comput. Math. 92(12), 2596\u20132614 (2015). doi:\n                        10.1080\/00207160.2015.1077948","journal-title":"Int. J. Comput. Math."},{"key":"272_CR25","doi-asserted-by":"publisher","unstructured":"Wang, Z., Vong, S., Lei, S.: Finite difference schemes for two-dimensional time-space fractional differential equations. Int. J. Comput. Math., 1\u201318 (2015). doi:\n                        10.1080\/00207160.2015.1009902","DOI":"10.1080\/00207160.2015.1009902"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0272-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0272-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0272-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T07:29:11Z","timestamp":1508830151000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0272-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,17]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["272"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0272-6","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,17]]}}}