{"id":"https://openalex.org/W2795615127","doi":"https://doi.org/10.1090/mcom/3571","title":"Geometry of error amplification in solving the Prony system with near-colliding nodes","display_name":"Geometry of error amplification in solving the Prony system with near-colliding nodes","publication_year":2020,"publication_date":"2020-09-09","ids":{"openalex":"https://openalex.org/W2795615127","doi":"https://doi.org/10.1090/mcom/3571","mag":"2795615127"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3571","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3571","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1701.04058","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036650421","display_name":"Andrey Akinshin","orcid":"https://orcid.org/0000-0003-3553-9367"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Andrey Akinshin","raw_affiliation_strings":["Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001823566","display_name":"Gil Goldman","orcid":"https://orcid.org/0000-0002-4087-7320"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Gil Goldman","raw_affiliation_strings":["Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052491254","display_name":"Yosef Yomdin","orcid":"https://orcid.org/0000-0003-3852-3440"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yosef Yomdin","raw_affiliation_strings":["Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036650421"],"corresponding_institution_ids":["https://openalex.org/I53964585"],"apc_list":null,"apc_paid":null,"fwci":0.8986,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67879908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"90","issue":"327","first_page":"267","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7650285959243774},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5950130224227905},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5786818265914917},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5726046562194824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5280647873878479},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4946078956127167},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46749603748321533},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4465722441673279},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42030957341194153},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3584267497062683},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33182263374328613},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32733309268951416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1493067741394043},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08375111222267151}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7650285959243774},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5950130224227905},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5786818265914917},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5726046562194824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5280647873878479},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4946078956127167},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46749603748321533},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4465722441673279},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42030957341194153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3584267497062683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33182263374328613},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32733309268951416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1493067741394043},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08375111222267151},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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":4,"locations":[{"id":"doi:10.1090/mcom/3571","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3571","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1701.04058","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.04058","pdf_url":"https://arxiv.org/pdf/1701.04058","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2795615127","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1701.04058","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1701.04058","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1701.04058","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1701.04058","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.04058","pdf_url":"https://arxiv.org/pdf/1701.04058","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W175556715","https://openalex.org/W210359992","https://openalex.org/W1480579230","https://openalex.org/W1554304031","https://openalex.org/W1559478034","https://openalex.org/W1639668784","https://openalex.org/W1786084726","https://openalex.org/W1946933104","https://openalex.org/W1978356474","https://openalex.org/W1991048140","https://openalex.org/W2010209436","https://openalex.org/W2015364553","https://openalex.org/W2018778093","https://openalex.org/W2022821885","https://openalex.org/W2041786636","https://openalex.org/W2049447905","https://openalex.org/W2058342765","https://openalex.org/W2061471690","https://openalex.org/W2068144942","https://openalex.org/W2071603349","https://openalex.org/W2089244156","https://openalex.org/W2093009076","https://openalex.org/W2113484718","https://openalex.org/W2114789426","https://openalex.org/W2119667497","https://openalex.org/W2139203673","https://openalex.org/W2158537680","https://openalex.org/W2168335598","https://openalex.org/W2191424897","https://openalex.org/W2508934708","https://openalex.org/W2578295578","https://openalex.org/W2617617174","https://openalex.org/W2755233754","https://openalex.org/W2904908797","https://openalex.org/W2938020605","https://openalex.org/W2949718909","https://openalex.org/W2950462555","https://openalex.org/W2950963611","https://openalex.org/W2950996929","https://openalex.org/W2961786997","https://openalex.org/W2962782658","https://openalex.org/W2962980983","https://openalex.org/W2963560677","https://openalex.org/W2963604884","https://openalex.org/W2988935227","https://openalex.org/W3006435741","https://openalex.org/W3082266491","https://openalex.org/W3101718007"],"related_works":["https://openalex.org/W2114789426","https://openalex.org/W2018778093","https://openalex.org/W2963373272","https://openalex.org/W2755233754","https://openalex.org/W2030858745","https://openalex.org/W2060929722","https://openalex.org/W1972401324","https://openalex.org/W3103531188","https://openalex.org/W2963270586","https://openalex.org/W2946339742","https://openalex.org/W2610857016","https://openalex.org/W109696764","https://openalex.org/W2073443629","https://openalex.org/W1800378265","https://openalex.org/W1969815718","https://openalex.org/W2134615334","https://openalex.org/W2951276273","https://openalex.org/W2796393871","https://openalex.org/W2017007913","https://openalex.org/W2604521278"],"abstract_inverted_index":{"We":[0,183],"consider":[1],"a":[2,23,45,313],"reconstruction":[3],"problem":[4,292],"for":[5],"\u201cspike-train\u201d":[6],"signals":[7],"<inline-formula":[8,27,122,188,218,268,301],"content-type=\"math/mathml\">":[9,28,123,189,219,269,302],"<mml:math":[10,29,124,190,220,270,303],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,30,125,191,221,271,304],"alttext=\"upper":[12,31],"F\">":[13],"<mml:semantics>":[14,59,148,200,234,275,346],"<mml:mi>F</mml:mi>":[15,61,156,167,208],"<mml:annotation":[16,110,177,212,253,283],"encoding=\"application/x-tex\">F</mml:annotation>":[17],"</mml:semantics>":[18,116,180,214,256,287],"</mml:math>":[19,117,181,215,257,288],"</inline-formula>":[20,118,182,216,258,289],"of":[21],"an":[22,263],"priori":[24],"known":[25,261],"form":[26],"F":[32,132,141,198,330],"left-parenthesis":[33,50,130,142,196,328],"x":[34,51,53,136,143,146,317],"right-parenthesis":[35,57,133,144,331],"equals":[36,40,134,223,308,323,334],"sigma-summation":[37],"Underscript":[38,306],"j":[39,47,55,307,315,319],"1":[41,226,309,337,344],"Overscript":[42,310],"d":[43,145,231,311,342],"Endscripts":[44,312],"Subscript":[46,54,127,193,314,318,325],"Baseline":[48,56,129,139,195,316,322,327],"delta":[49],"minus":[52,232,343],"comma\">":[58],"<mml:mrow>":[60,93,149,201,235,276,347],"<mml:mo":[62,65,154,157,168,171,206,209],"stretchy=\"false\">(</mml:mo>":[63,155,169,207],"<mml:mi>x</mml:mi>":[64,95,100,164,170,174,365],"stretchy=\"false\">)</mml:mo>":[66,158,172,210],"<mml:mo>=</mml:mo>":[67,75,159,237,355,369],"<mml:munderover>":[68,348],"<mml:mo>":[69,96,160,242,248,349],"\u2211":[70,350],"</mml:mo>":[71,98,162,244,250,351],"<mml:mrow":[72,78,85,101,352],"class=\"MJX-TeXAtom-ORD\">":[73,79,86,102,353],"<mml:mi>j</mml:mi>":[74,87,103,354,362,366],"<mml:mn>1</mml:mn>":[76,240,251,356],"</mml:mrow>":[77,81,88,104,107,109,176,211,252,282,357],"<mml:mi>d</mml:mi>":[80,173,247,358],"</mml:munderover>":[82,359],"<mml:msub>":[83,99,150,202,360,370],"<mml:mi>a</mml:mi>":[84,361],"</mml:msub>":[89,105,153,205,363,373],"<mml:mi>":[90,277],"\u03b4":[91],"</mml:mi>":[92,279],"<mml:mo>(</mml:mo>":[94],"\u2212":[97,249],"<mml:mo>)</mml:mo>":[106],"<mml:mo>,</mml:mo>":[108,239,241,245],"encoding=\"application/x-tex\">F(x)=\\sum":[111],"_{j=1}^{d}a_{j}\\delta":[112],"\\left":[113],"(x-x_{j}\\right":[114],"),</mml:annotation>":[115],"from":[119],"their":[120],"moments":[121,187],"alttext=\"m":[126,192],"k":[128,138,194,321,326,333],"upper":[131,140,197,329],"integral":[135],"Superscript":[137,320],"period\">":[147,345],"<mml:mi>m</mml:mi>":[151,203,371],"<mml:mi>k</mml:mi>":[152,165,204,236,367,372],"\u222b":[161],"<mml:msup>":[163],"</mml:msup>":[166],"<mml:mo>.</mml:mo>":[175],"encoding=\"application/x-tex\">m_k(F)=\\int":[178],"x^kF(x)dx.</mml:annotation>":[179],"assume":[184],"that":[185],"the":[186,298],"right-parenthesis\">":[199],"encoding=\"application/x-tex\">m_k(F)</mml:annotation>":[213],",":[217,259],"alttext=\"k":[222],"0":[224,335],"comma":[225,227,229,332,336,338,340],"ellipsis":[228,339],"2":[230,341],"1\">":[233],"<mml:mn>0</mml:mn>":[238,281],"\u2026":[243],"<mml:mn>2</mml:mn>":[246],"encoding=\"application/x-tex\">k=0,1,\\ldots":[254],",2d-1</mml:annotation>":[255],"are":[260],"with":[262],"absolute":[264],"error":[265],"not":[266],"exceeding":[267],"alttext=\"epsilon":[272],"greater-than":[273],"0\">":[274],"\u03f5":[278],"<mml:mo>&gt;</mml:mo>":[280],"encoding=\"application/x-tex\">\\epsilon":[284],"&gt;":[285],"0</mml:annotation>":[286],".":[290],"This":[291],"is":[293],"essentially":[294],"equivalent":[295],"to":[296],"solving":[297],"Prony":[299],"system":[300],"alttext=\"sigma-summation":[305],"m":[324],"<mml:msubsup>":[364],"</mml:msubsup>":[368]},"counts_by_year":[{"year":2020,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2025-10-10T00:00:00"}