{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,22]],"date-time":"2023-11-22T02:52:44Z","timestamp":1700621564242},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[1980,9,1]],"date-time":"1980-09-01T00:00:00Z","timestamp":336614400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Zeitschrift f\u00fcr Operations Research"],"published-print":{"date-parts":[[1980,9]]},"DOI":"10.1007\/bf01919243","type":"journal-article","created":{"date-parts":[[2005,7,25]],"date-time":"2005-07-25T10:11:52Z","timestamp":1122286312000},"page":"155-170","source":"Crossref","is-referenced-by-count":4,"title":["Improved iterative computation of the expected discounted return in Markov and semi-Markov chains"],"prefix":"10.1007","volume":"24","author":[{"given":"E. L.","family":"Porteus","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF01919243_CR1","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1137\/1009030","volume":"9","author":"E. Denardo","year":"1967","unstructured":"Denardo, E.: Contraction mappings in the theory underlying dynamic programming, SIAM Review9, 1967, 165\u2013177.","journal-title":"SIAM Review"},{"key":"BF01919243_CR2","unstructured":"Doob, J.: Stochastic Processes. New York 1953."},{"key":"BF01919243_CR3","unstructured":"Federgruen, A., andP. Schweitzer: A survey of asymptotic value-iteration for undiscounted Markovian decision processes. To appear in: Ed. by D. White. Proc. Intl. Conf. on Markov Decision Processes. Manchester 1979."},{"key":"BF01919243_CR4","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1016\/0022-247X(78)90174-9","volume":"65","author":"A. Federgruen","year":"1978","unstructured":"Federgruen, A., P. Schweitzer, andH. Tijms: Contraction mappings underlying undiscounted Markov decision problems. J. Math. Anal. Appl.65, 1978, 711\u2013730.","journal-title":"J. Math. Anal. Appl."},{"key":"BF01919243_CR5","unstructured":"Fox, L.: Finite-difference methods for elliptic boundary-value problems. The State of the Art in Numerical Analysis. Ed. by D. Jacobs. London-New York 1977, 799\u2013881."},{"key":"BF01919243_CR6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1017\/S0305004100030991","volume":"52","author":"J. Hajnal","year":"1956","unstructured":"Hajnal, J.: The ergodic properties of nonhomogeneous Markov chains, Proc. Cambridge Phil. Soc.52, 1956, 67\u201377.","journal-title":"Proc. Cambridge Phil. Soc."},{"key":"BF01919243_CR7","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1017\/S0305004100033399","volume":"54","author":"J. Hajnal","year":"1958","unstructured":"\u2014: Weak ergodicity in nonhomogeneous Markov chains. Proc. Cambridge Phil. Soc.54, 1958, 233\u2013246.","journal-title":"Proc. Cambridge Phil. Soc."},{"key":"BF01919243_CR8","unstructured":"van Hee, K., A. Hordijk, andJ. van der Wahl: Successive approximations for convergent dynamic programming. Ed. by H. Tijms and J. Wessels. Markov Decision Theory. Math. Centre Tract 93, Amsterdam 1977, 183\u2013212."},{"key":"BF01919243_CR9","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0022-247X(76)90288-2","volume":"55","author":"K. Hinderer","year":"1976","unstructured":"Hinderer, K.: Estimates for finite-stage dynamic programs. J. Math. Anal. Appl.55, 1976, 207\u2013238.","journal-title":"J. Math. Anal. Appl."},{"key":"BF01919243_CR10","unstructured":"-: On approximate solutions of finite stage dynamic programs. Ed. by M. Puterman. Dynamic Programming and Its Application, New York 1978."},{"key":"BF01919243_CR11","unstructured":"Hinderer, K., andG. H\u00fcbner: On exact and approximate solutions of unstructured finite-stage dynamic programs. Ed. by H. Tijms and J. Wessels. Markov Decision Theory. Math. Centre Tract 93, Amsterdam 1977, 57\u201376."},{"key":"BF01919243_CR12","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1002\/nav.3800170210","volume":"17","author":"D. Hitchcock","year":"1970","unstructured":"Hitchcock, D., andJ. MacQueen: On computing the expected discounted return in a Markov chain. Naval Res. Logist. Quart.17, 1970, 237\u2013241.","journal-title":"Naval Res. Logist. Quart."},{"key":"BF01919243_CR13","unstructured":"Howard, R.: Dynamic Programming and Markov Processes. New York 1960."},{"key":"BF01919243_CR14","first-page":"57","volume":"98","author":"G. H\u00fcbner","year":"1977","unstructured":"H\u00fcbner, G.: Contraction properties of Markov decision models with applications to the elimination of non-optimal actions. Dynamische Optimierung, Bonner Math. Schriften98, 1977, 57\u201365.","journal-title":"Dynamische Optimierung, Bonner Math. Schriften"},{"key":"BF01919243_CR15","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1287\/opre.11.6.938","volume":"11","author":"W. Jewell","year":"1963","unstructured":"Jewell, W.: Markov-renewal programming. I: Formulation, finite return models. Opns. Res.11, 1963, 938\u2013948.","journal-title":"Opns. Res."},{"key":"BF01919243_CR16","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/0022-247X(66)90060-6","volume":"14","author":"J. MacQueen","year":"1966","unstructured":"MacQueen, J.: A modified dynamic programming method for Markovian decision problems. J. Math. Anal. Appl.14, 1966, 38\u201343.","journal-title":"J. Math. Anal. Appl."},{"key":"BF01919243_CR17","volume-title":"Report Nr. 244","author":"L. McDowell","year":"1967","unstructured":"McDowell, L.: Variable Successive Over-Relaxation. Report Nr. 244, Department of Computer Science, University of Illinois, Urbana, Illinois, 1967."},{"key":"BF01919243_CR18","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1287\/opre.19.1.244","volume":"19","author":"T. Morton","year":"1971","unstructured":"Morton, T.: On the asymptotic convergence rate of cost difference for Markovian decision processes. Opns. Res.19, 1971a, 244\u2013248.","journal-title":"Opns. Res."},{"key":"BF01919243_CR19","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1287\/opre.19.4.1081","volume":"19","author":"T. Morton","year":"1971","unstructured":"\u2014: Undiscounted Markov renewal programming via modified successive approximations. Opns. Res.19, 1971b, 1081\u20131089.","journal-title":"Opns. Res."},{"key":"BF01919243_CR20","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1287\/mnsc.23.8.890","volume":"23","author":"T. Morton","year":"1977","unstructured":"Morton, T., andW. Wecker: Discounting, ergodicity, and convergence for Markov decision provesses. Man. Sci.23, 1977, 890\u2013900.","journal-title":"Man. Sci."},{"key":"BF01919243_CR21","first-page":"203","volume":"20","author":"J. Nunen van","year":"1976","unstructured":"van Nunen, J.: A set of successive approximation methods for discounted Markovian decision problems. Z. Opns. Res.20, 1976a, 203\u2013208.","journal-title":"Z. Opns. Res."},{"key":"BF01919243_CR22","unstructured":"-: Contracting Markov Decision Processes. Math. Centre Tract 71, Amsterdam 1976a."},{"key":"BF01919243_CR23","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1287\/mnsc.18.1.7","volume":"18","author":"E. Porteus","year":"1971","unstructured":"Porteus, E.: Some bounds for discounted sequential decision processes. Man. Sci.18, 1971, 7\u201311.","journal-title":"Man. Sci."},{"key":"BF01919243_CR24","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1287\/opre.23.4.761","volume":"23","author":"E. Porteus","year":"1975","unstructured":"\u2014: Bounds and transformations for finite Markov decision chains, Opns. Res.23, 1975, 761\u2013784.","journal-title":"Opns. Res."},{"key":"BF01919243_CR25","unstructured":"-: Overview of iterative methods for discounted finite Markov and semi-markov decision chains. To appear. Ed. by D. White. Intl. Conf. on Markov Decision Processes. Manchester 1979a."},{"key":"BF01919243_CR26","unstructured":"-: Improved iterative computation of the expected discounted return in Markov and semi-Markov chains. Research Paper 443 Rev., Graduate School of Business, Stanford University, 1979b."},{"key":"BF01919243_CR27","unstructured":"Porteus, E., andJ. Totten: An experiment in computing the expected discounted return in a finite Markov chain. Research Paper 250, Graduate School of Business, Stanford University, 1975."},{"key":"BF01919243_CR28","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1287\/opre.26.2.350","volume":"26","author":"E. Porteus","year":"1978","unstructured":"\u2014: Accelerated computation of the expected discounted return in a Markov chain. Opns. Res.26, 1978, 350\u2013358.","journal-title":"Opns. Res."},{"key":"BF01919243_CR29","first-page":"1127","volume":"24","author":"M. Puterman","year":"1978","unstructured":"Puterman, M., andM. Shin: Modified policy iteration algorithms for discounted Markov decision problems24, 1978, 1127\u20131137.","journal-title":"Modified policy iteration algorithms for discounted Markov decision problems"},{"key":"BF01919243_CR30","first-page":"125","volume":"20","author":"D. Reetz","year":"1976","unstructured":"Reetz, D.: Decision exclusion algorithm for a class of Markovian decision processes. Z. Opns. Res.20, 1976, 125\u2013131.","journal-title":"Z. Opns. Res."},{"key":"BF01919243_CR31","unstructured":"Reid, J.: Sparse matrices. Ed. by D. Jacobs. The State of the Art in Numerical Analysis. New York 1977, 85\u2013148."},{"key":"BF01919243_CR32","unstructured":"Rothblum, U.: Iterated successive approximation for sequential decision processes. New Haven 1979."},{"key":"BF01919243_CR33","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/0022-247X(71)90094-1","volume":"34","author":"P. Schweitzer","year":"1971","unstructured":"Schweitzer, P.: Iterative solution of the functional equations of undiscounted Markov renewal programming. J. Math. Anal. Appl.34, 1971, 495\u2013501.","journal-title":"J. Math. Anal. Appl."},{"key":"BF01919243_CR34","doi-asserted-by":"crossref","first-page":"188","DOI":"10.2307\/1426774","volume":"11","author":"P. Schweitzer","year":"1979","unstructured":"Schweitzer, P., andA. Federgruen: Geometric convergence of value-iteration in multichain Markov renewal programming. Adv. Appl. Prob.11, 1979, 188\u2013217.","journal-title":"Adv. Appl. Prob."},{"key":"BF01919243_CR35","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1137\/0710046","volume":"10","author":"A. Settari","year":"1973","unstructured":"Settari, A., andK. Aziz: A generalization of the additive correction methods for the iterative solution of matrix equations. SIAM J. Numer. Anal.10, 1973, 506\u2013521.","journal-title":"SIAM J. Numer. Anal."},{"key":"BF01919243_CR36","unstructured":"Varga, R.: Matrix Iterative Analysis. Englewood Cliffs 1962."},{"key":"BF01919243_CR37","unstructured":"Verkhovsky, B.: Smoothing system design and parametric Markovian programming. Ed. by H. Tijms and J. Wessels. Markov Decision Theory. Math. Centre Tract 93, Amsterdam 1977, 105\u2013117."},{"key":"BF01919243_CR38","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF02276760","volume":"17","author":"J. Wal van der","year":"1976","unstructured":"van der Wal, J.: A successive approximation algorithm for an undiscounted Markov decision process, Computing17, 1976, 157\u2013162.","journal-title":"Computing"},{"key":"BF01919243_CR39","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF00933260","volume":"25","author":"J. Wal van der","year":"1978","unstructured":"\u2014: Discounted Markov games: generalized policy iteration method. J. Optzn. Th. Appl.25, 1978, 125\u2013138.","journal-title":"J. Optzn. Th. Appl."},{"key":"BF01919243_CR40","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/0022-247X(63)90017-9","volume":"6","author":"D. White","year":"1963","unstructured":"White, D.: Dynamic programming, Markov chains and the method of successive approximations. J. Math. Anal. Appl.6, 1963, 373\u2013376.","journal-title":"J. Math. Anal. Appl."},{"key":"BF01919243_CR41","unstructured":"Young, D.: Iterative Solution of Large Linear Systems. New York 1971."},{"key":"BF01919243_CR42","unstructured":"Young, D., andR. Gregory: A Survey of Numerical Mathematics. Reading 1973."}],"container-title":["Zeitschrift f\u00fcr Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01919243.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01919243\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01919243","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T20:32:43Z","timestamp":1557433963000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01919243"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1980,9]]},"references-count":42,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1980,9]]}},"alternative-id":["BF01919243"],"URL":"https:\/\/doi.org\/10.1007\/bf01919243","relation":{},"ISSN":["0340-9422","1432-5217"],"issn-type":[{"value":"0340-9422","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[1980,9]]}}}