Title Improved solution enclosures for over- and underdetermined interval linear systems Author E. D. Popova Journal / Anthology LARGE-SCALE SCIENTIFIC COMPUTING LECTURE NOTES IN COMPUTER SCIENCE
 Year: 2006
 Volume: 3743
 Page range: 305-312 Description In this paper we discuss an inclusion method for solving rectangular (over- and under-determined) dense linear systems where the input data are uncertain and vary within given intervals. An improvement of the quality of the solution enclosures is described for both independent and parameter dependent input intervals. A fixed-point algorithm with result verification that exploits the structure of the problems to be solved is given. Mathematica functions for solving the discussed rectangular problems are developed and presented. Numerical examples illustrate the advantages of the proposed improved approach. Subjects Applied Mathematics > Optimization Mathematics > Algebra > Linear Algebra Keywords overdetermined interval linear systems, underdetermined interval linear systems, regular dense linear systems
{"ft_lang_label":"__label__en","ft_lang_prob":0.79365456,"math_prob":0.8523778,"size":950,"snap":"2019-51-2020-05","text_gpt3_token_len":191,"char_repetition_ratio":0.18498942,"word_repetition_ratio":0.13333334,"special_character_ratio":0.21894737,"punctuation_ratio":0.05511811,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96217704,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-21T17:25:09Z\",\"WARC-Record-ID\":\"<urn:uuid:4129f610-eeaf-40ad-abc1-e497446a8861>\",\"Content-Length\":\"52494\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3a2a22c0-a813-44a1-89ad-1e407c3a83de>\",\"WARC-Concurrent-To\":\"<urn:uuid:21aaf4a6-5e86-4193-9327-3eeaa96a998d>\",\"WARC-IP-Address\":\"140.177.205.65\",\"WARC-Target-URI\":\"https://library.wolfram.com/infocenter/Articles/6245/\",\"WARC-Payload-Digest\":\"sha1:XR5A2W6QJN323G3I4OMUVUNMZHL5LC5M\",\"WARC-Block-Digest\":\"sha1:O6RX2WUQRXR5DJCMRNG4RKHWZERWVIPA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250604849.31_warc_CC-MAIN-20200121162615-20200121191615-00473.warc.gz\"}"}