{"id":"https://openalex.org/W2061292372","doi":"https://doi.org/10.1002/(sici)1099-1506(199611/12)3:6<513::aid-nla93>3.0.co;2-4","title":"Piecewise Polynomial Solutions Without a priori Break Points","display_name":"Piecewise Polynomial Solutions Without a priori Break Points","publication_year":1996,"publication_date":"1996-11-01","ids":{"openalex":"https://openalex.org/W2061292372","doi":"https://doi.org/10.1002/(sici)1099-1506(199611/12)3:6<513::aid-nla93>3.0.co;2-4","mag":"2061292372"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199611/12)3:6<513::aid-nla93>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199611/12)3:6<513::aid-nla93>3.0.co;2-4","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039737516","display_name":"Per Christian Hansen","orcid":"https://orcid.org/0000-0002-7333-7216"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Per Christian Hansen","raw_affiliation_strings":["UNI\u2022C, Building 304, Technical University of Denmark, DK-2800 Lyngby, Denmark","UNI\u2022C, Building 304 Technical University of Denmark DK-2800 Lyngby, Denmark"],"affiliations":[{"raw_affiliation_string":"UNI\u2022C, Building 304, Technical University of Denmark, DK-2800 Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"UNI\u2022C, Building 304 Technical University of Denmark DK-2800 Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016855562","display_name":"Klaus Mosegaard","orcid":"https://orcid.org/0000-0001-5292-5249"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Klaus Mosegaard","raw_affiliation_strings":["Niels bohr Institute for Astronomy, Physics and Geophysics, Copenhagen University, Juliane Maries Vej 30, DK-2100 Copenhagen \u00d8, Denmark","Niels bohr Institute for Astronomy, Physics and Geophysics, Copenhagen University, Juliane Maries Vej 30, DK\u20102100 Copenhagen \u00d8, Denmark"],"affiliations":[{"raw_affiliation_string":"Niels bohr Institute for Astronomy, Physics and Geophysics, Copenhagen University, Juliane Maries Vej 30, DK-2100 Copenhagen \u00d8, Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"Niels bohr Institute for Astronomy, Physics and Geophysics, Copenhagen University, Juliane Maries Vej 30, DK\u20102100 Copenhagen \u00d8, Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039737516"],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.556,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.62816081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"3","issue":"6","first_page":"513","last_page":"524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10716","display_name":"Soil and Unsaturated Flow","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.9446438550949097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7391573786735535},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6796244382858276},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.6781134009361267},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6171629428863525},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5920116305351257},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5835153460502625},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5165623426437378},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46094805002212524},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32265979051589966},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24543046951293945},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1404971182346344}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.9446438550949097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7391573786735535},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6796244382858276},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6781134009361267},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6171629428863525},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5920116305351257},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5835153460502625},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5165623426437378},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46094805002212524},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32265979051589966},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24543046951293945},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1404971182346344},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199611/12)3:6<513::aid-nla93>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199611/12)3:6<513::aid-nla93>3.0.co;2-4","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1485489034","https://openalex.org/W1616398893","https://openalex.org/W1653357460","https://openalex.org/W1980688227","https://openalex.org/W2033242948","https://openalex.org/W2037099387","https://openalex.org/W2045596450","https://openalex.org/W2048245744","https://openalex.org/W2075894130","https://openalex.org/W2167400582","https://openalex.org/W2168335598","https://openalex.org/W2398004379","https://openalex.org/W2595831298","https://openalex.org/W4214677270","https://openalex.org/W6637005875","https://openalex.org/W6685002216","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W3125305985","https://openalex.org/W3098629791","https://openalex.org/W2107099361","https://openalex.org/W2051018371","https://openalex.org/W2049021870","https://openalex.org/W4232993046","https://openalex.org/W2099017078","https://openalex.org/W2165081943","https://openalex.org/W3023398579","https://openalex.org/W1633967447"],"abstract_inverted_index":{"In":[0,73],"certain":[1],"inverse":[2],"problems":[3],"it":[4],"is":[5,55,69,82],"useful":[6],"to":[7,10,27,45,93],"be":[8],"able":[9],"compute":[11,28],"solutions":[12,29,42,86],"which":[13,30,81],"are,":[14],"in":[15],"some":[16],"sense,":[17],"as":[18,20,36,39],"simple":[19],"possible.":[21,40],"For":[22],"example,k":[23],"one":[24],"may":[25],"wish":[26],"are":[31,43,88],"piecewise":[32,66,70,89],"constant":[33,67],"and":[34],"with":[35],"few":[37],"discontinuities":[38],"Such":[41],"suited":[44],"describe":[46],"models,":[47],"e.g.,":[48],"geological":[49],"layers,":[50],"where":[51],"the":[52,59,97,100,104],"coarse":[53],"structure":[54],"more":[56],"important":[57],"than":[58],"fine":[60],"structure.":[61],"A":[62],"natural":[63],"generalization":[64],"of":[65,84,99],"functions":[68],"polynomial":[71,105],"solutions.":[72],"this":[74],"paper":[75],"we":[76],"present":[77],"a":[78,95],"new":[79],"algorithm":[80],"capable":[83],"computing":[85],"that":[87],"polynomials,":[90],"without":[91],"having":[92],"specify":[94],"priori":[96],"positions":[98],"break":[101],"points":[102],"between":[103],"pieces.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}