{"id":"https://openalex.org/W2484861975","doi":"https://doi.org/10.1007/978-3-322-87426-9_5","title":"Interpolation und diskrete Approximation","display_name":"Interpolation und diskrete Approximation","publication_year":1981,"publication_date":"1981-01-01","ids":{"openalex":"https://openalex.org/W2484861975","doi":"https://doi.org/10.1007/978-3-322-87426-9_5","mag":"2484861975"},"language":"de","primary_location":{"id":"doi:10.1007/978-3-322-87426-9_5","doi":"https://doi.org/10.1007/978-3-322-87426-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-322-87426-9_5","pdf_url":null,"source":{"id":"https://openalex.org/S4306464255","display_name":"Vieweg+Teubner eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4238967321","display_name":"Numerische Mathematik"},"type":"book-chapter","is_traditional":true,"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/A5067206938","display_name":"J\u00fcrgen Kahmann","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J\u00fcrgen Kahmann","raw_affiliation_strings":["Wolfenb\u00fcttel, Deutschland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wolfenb\u00fcttel, Deutschland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5067206938"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31800263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"104","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9721999764442444,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9721999764442444,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13806","display_name":"Mathematical and Computational Methods","score":0.011699999682605267,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.004000000189989805,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"polynomial interpolation","score":0.8889999985694885},{"id":"https://openalex.org/keywords/lagrange-polynomials","display_name":"Lagrange polynomials","score":0.8920000195503235},{"id":"https://openalex.org/keywords/interpolation-polynomials","display_name":"interpolation polynomials","score":0.7609999775886536},{"id":"https://openalex.org/keywords/discrete-approximation","display_name":"discrete approximation","score":0.8999999761581421},{"id":"https://openalex.org/keywords/interpolation-error","display_name":"interpolation error","score":0.5139999985694885}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5730522871017456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43502163887023926},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4285699129104614},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.3327248692512512},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09696939587593079}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-322-87426-9_5","doi":"https://doi.org/10.1007/978-3-322-87426-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-322-87426-9_5","pdf_url":null,"source":{"id":"https://openalex.org/S4306464255","display_name":"Vieweg+Teubner eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2560682138","https://openalex.org/W4246930641","https://openalex.org/W4247284411","https://openalex.org/W4231056828","https://openalex.org/W4312826909","https://openalex.org/W38030987","https://openalex.org/W4212929382","https://openalex.org/W6922773072","https://openalex.org/W2964353988","https://openalex.org/W2790902669"],"abstract_inverted_index":{"ZusammenfassungZu":[0],"gegebenen":[1],"St\u00fctzstellen":[2,57],"xo,...,":[3,58],"xn":[4,59],"bilden":[5],"die":[6,69,73],"Lagrange-Polynome":[7],"$$":[8,53],"{{l}_{i}}\\left(":[9,94],"x":[10],"\\right)=\\frac{\\left(":[11],"x-{{x}_{o}}":[12],"\\right)\\ldots":[13,18,23,28],"\\left(":[14,19,24,29],"x-{{x}_{i-1}}":[15],"\\right)\\left(":[16,26],"x-{{x}_{i+1}}":[17],"x-{{x}_{n}}":[20],"\\right)}{\\left(":[21],"{{x}_{i}}-{{x}_{o}}":[22],"{{x}_{i}}-{{x}_{i-1}}":[25],"{{x}_{i}}-{{x}_{i+1}}":[27],"{{x}_{i}}-{{x}_{n}}":[30],"\\right)}$$":[31],"eine":[32],"Basis":[33],"im":[34],"Vektorraum":[35],"der":[36],"Polynome":[37],"bis":[38],"zunn":[39],"Grau":[40],"n.":[41],"Es":[42],"ist":[43,90],"$${{l}_{i}}\\left(":[44],"{{x}_{k}}":[45,92,95],"\\right)={{\\delta":[46],"}_{ik}}=\\left\\{":[47],"_{0}^{1}":[48],"\\right.":[49],"f\\ddot{u}r":[50],"_{i\\ne":[51],"k}^{i=k}":[52],"Sind":[54],"zu":[55],"den":[56],"St\u00fctzwerte":[60],"fo,...,":[61],"fn":[62,84],"gegeben,":[63],"dann":[64],"hat":[65],"das":[66],"Interpolationspolynom":[67],"durch":[68],"Knoten":[70],"(xi,":[71],"fi)":[72],"Form":[74],"(*)":[75],"pol":[76],"(x)":[77,82],"=":[78],"fo":[79],"\u00b7":[80,85],"lo":[81],"+...+":[83],"ln":[86],"(x),":[87],"denn":[88],"es":[89],"$$pol\\left(":[91],"\\right)=\\sum\\limits_{i=0}^{n}{{{f}_{i}}}\\cdot":[93,96],"{{\\delta":[97],"}_{ik}}={{f}_{k}}$$.":[98]},"counts_by_year":[],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2016-08-23T00:00:00"}
