{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T14:24:42Z","timestamp":1698330282148},"reference-count":20,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,12,13]],"date-time":"2006-12-13T00:00:00Z","timestamp":1165968000000},"content-version":"vor","delay-in-days":4790,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory & Apps"],"published-print":{"date-parts":[[1993,11]]},"abstract":"Abstract<\/jats:title>This paper deals with the so\u2010called tangential Nevanlinna\u2014Pick interpolation problem for bounded real matrices. This problem can be formulated as follows: given a set of n<\/jats:italic> pairs {(p<\/jats:italic>i<\/jats:italic><\/jats:sub>,K<\/jats:bold>i<\/jats:italic><\/jats:sub>)}, where p<\/jats:italic>i<\/jats:sub> are distinct complex numbers with Re p<\/jats:italic>i<\/jats:italic><\/jats:sub> > 0 and K<\/jats:bold>i<\/jats:italic><\/jats:sub> stands for 2m<\/jats:italic> \u00d7 l<\/jats:italic>i<\/jats:italic><\/jats:sub> constant matrices, assuming that for every pair (p<\/jats:italic>i<\/jats:italic><\/jats:sub>, K<\/jats:bold>i<\/jats:italic><\/jats:sub>) with p<\/jats:italic>i<\/jats:italic><\/jats:sub> complex there exists a complex conjugate pair (p<\/jats:italic><\/jats:styled-content>i<\/jats:italic><\/jats:sub>, K<\/jats:bold><\/jats:styled-content>i<\/jats:italic><\/jats:sub>) and that for every pair (p<\/jats:italic>i<\/jats:italic><\/jats:sub>, K<\/jats:bold>i<\/jats:italic><\/jats:sub>) in which p<\/jats:italic>i<\/jats:italic><\/jats:sub> is real K<\/jats:bold>i<\/jats:italic><\/jats:sub> is also real, find an m \u00d7 m<\/jats:italic> bounded real matrix S(p)<\/jats:italic> such that [S<\/jats:bold>(p<\/jats:italic>i<\/jats:italic><\/jats:sub>) 1m<\/jats:italic><\/jats:sub>]K<\/jats:bold>i<\/jats:italic><\/jats:sub> = 0 for i<\/jats:italic>= 1,\u2026,n<\/jats:italic>.<\/jats:p>The solution of this problem is obtained in an inductive way through the construction at each step of a real lossless multiport section that realizes two complex conjugate pairs or one real pair. After each step the number of pairs (p<\/jats:italic>i<\/jats:italic><\/jats:sub>, K<\/jats:bold>i<\/jats:italic><\/jats:sub>) is reduced by two (if p<\/jats:italic>i<\/jats:italic><\/jats:sub> is complex) or by one (if p<\/jats:italic>i<\/jats:italic><\/jats:sub> is real). the procedure is continued until all pairs have been considered. After the last step the final section may be terminated with any bounded real load. the scattering matrix S<\/jats:bold>(p<\/jats:italic>) of the resulting cascade multiport network is bounded real and satisfies the desired interpolation conditions. In this way the tangential interpolation problem is reduced to classical network cascade synthesis by the use of real lossless multiport sections.<\/jats:p>","DOI":"10.1002\/cta.4490210603","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T09:57:09Z","timestamp":1183370229000},"page":"513-538","source":"Crossref","is-referenced-by-count":1,"title":["Tangential nevanlinna\u2010pick interpolation problem for bounded real matrices\u2014A network approach"],"prefix":"10.1002","volume":"21","author":[{"given":"Marian S.","family":"Piekarski","sequence":"first","affiliation":[]},{"given":"Marceli","family":"Uruski","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,12,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490090203"},{"key":"e_1_2_1_3_2","unstructured":"C. V. 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Nauk Armjan SSR"},{"key":"e_1_2_1_13_2","first-page":"214","article-title":"Tangential Nevanlinna\u2010Pick problem with multiple points","volume":"61","author":"Fedcina I. P.","year":"1975","journal-title":"Dokl. Akad. Nauk Armjan SSR"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0136005"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1137\/0136004"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(90)90064-P"},{"key":"e_1_2_1_17_2","volume-title":"Theory of Matrices","author":"Gantmacher F. R.","year":"1959"},{"key":"e_1_2_1_18_2","volume-title":"Linear Multiport Synthesis","author":"Newcomb R. W.","year":"1966"},{"key":"e_1_2_1_19_2","volume-title":"Classical Network Theory","author":"Belevitch B.","year":"1968"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1961.1057636"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.4490210603","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.4490210603","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T19:10:00Z","timestamp":1698174600000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.4490210603"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,11]]},"references-count":20,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1993,11]]}},"alternative-id":["10.1002\/cta.4490210603"],"URL":"https:\/\/doi.org\/10.1002\/cta.4490210603","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,11]]}}}