{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T12:03:08Z","timestamp":1648814588869},"reference-count":9,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[1970,7]]},"abstract":"\n The Fredholm integral equation where the kernel is semidegenerate has many applications. The solution of this integral equation may be studied as a function of the upper limit of integration\n x<\/jats:italic>\n , while\n t<\/jats:italic>\n remains fixed. It is shown that the solution satisfies an initial-value problem. This reformulation is well suited to numerical solution by analog and digital computers.\n <\/jats:p>\n The present paper is one of a series on initial-value methods for Fredholm integral equations. Its considerations are of practical significance since an arbitrary kernel may be approximated by a degenerate kernel to a desired degree of accuracy using standard techniques. Furthermore, the important cases in which the kernel is a Green's function and in which the integral equation is a Volterra equation are both covered by this treatment.<\/jats:p>","DOI":"10.1145\/321592.321594","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:26:10Z","timestamp":1027769170000},"page":"412-419","source":"Crossref","is-referenced-by-count":24,"title":["An Initial-Value Theory for Fredholm Integral Equations With Semidegenerate Kernels"],"prefix":"10.1145","volume":"17","author":[{"given":"H. H.","family":"Kagiwada","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Southern California, Los Angeles, California and The RAND Corporation, Santa Monica, California"}]},{"given":"R.","family":"Kalaba","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Southern California, Los Angeles, California and The RAND Corporation, Santa Monica, California"}]}],"member":"320","reference":[{"key":"e_1_2_1_1_2","unstructured":"KA6IWADA H. H. AND KALABA R.E. An initial-value method for Fredholm integral' equations of convolution type. Int. J. Comp. Math. (to appear). KA6IWADA H. H. AND KALABA R.E. An initial-value method for Fredholm integral' equations of convolution type. Int. J. Comp. Math. (to appear)."},{"key":"e_1_2_1_2_2","first-page":"1","article-title":"An initial-value method suitable for the computation of certain Fredholm resolvents","volume":"1","author":"KA WADA","year":"1967","journal-title":"J. Math. Phys. Sci."},{"key":"e_1_2_1_3_2","first-page":"322","article-title":"Initial-value methods for the basic boundary value problem and integra~ equation of radiative transfer","volume":"3","author":"KA WADA","year":"1967","journal-title":"J. Comp. Phys. I"},{"key":"e_1_2_1_4_2","first-page":"1","article-title":"An initial-value method for Fredholm integral equations","volume":"19","author":"SCHUMITZKY A","year":"1967","journal-title":"J. Math. Anal. Appl."},{"key":"e_1_2_1_5_2","volume-title":"Calif.","author":"UENO S.","year":"1968"},{"key":"e_1_2_1_6_2","first-page":"3","article-title":"Numerical results for the auxiliary equation of radiative transfer","volume":"6","author":"BELLMAN R. E.","year":"1966","journal-title":"J. Quant. Spect. Radiat. Transfer"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1086\/149000","article-title":"A new initial-value method for internal intensities in radiative transfer","volume":"147","author":"KAGIWADA H. H.","year":"1967","journal-title":"Astrophys. J."},{"key":"e_1_2_1_8_2","volume-title":"Calif.","author":"BUELL J.","year":"1968"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00932553","article-title":"A practical method for determining Green's functions using Hadamard's variational formula","volume":"1","author":"KAGIWADA H. H.","year":"1967","journal-title":"J. Optimization Theory Appl."}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/321592.321594","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T17:52:24Z","timestamp":1614707544000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/321592.321594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1970,7]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1970,7]]}},"alternative-id":["10.1145\/321592.321594"],"URL":"http:\/\/dx.doi.org\/10.1145\/321592.321594","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"value":"0004-5411","type":"print"},{"value":"1557-735X","type":"electronic"}],"subject":["Artificial Intelligence","Hardware and Architecture","Information Systems","Control and Systems Engineering","Software"],"published":{"date-parts":[[1970,7]]}}}