{"id":"https://openalex.org/W7164867137","doi":"https://doi.org/10.48550/arxiv.2606.13827","title":"Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds","display_name":"Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds","publication_year":2026,"publication_date":"2026-06-11","ids":{"openalex":"https://openalex.org/W7164867137","doi":"https://doi.org/10.48550/arxiv.2606.13827"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.13827","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13827","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.13827","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016234200","display_name":"Srinivas Nambirajan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nambirajan, Srinivas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5016234200"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.26669999957084656,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.26669999957084656,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.1404000073671341,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.12309999763965607,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6266999840736389},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5454999804496765},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.4756999909877777},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4399000108242035},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.41339999437332153},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.39250001311302185},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.3871999979019165},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.3716999888420105},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.32919999957084656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7799000144004822},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6266999840736389},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5454999804496765},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5317999720573425},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.4756999909877777},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4399000108242035},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3871999979019165},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35530000925064087},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3221000134944916},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.28540000319480896},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.28519999980926514},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28110000491142273},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.27459999918937683},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.273499995470047},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.2529999911785126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.13827","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13827","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.13827","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13827","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Markovian":[0],"Whittle-Mat\u00e9rn":[1],"fields":[2,67],"have":[3],"been":[4],"convergently":[5],"approximated":[6],"by":[7,210],"discrete":[8],"Gauss":[9],"Markov":[10],"Random":[11],"Fields":[12],"(GMRFs)":[13],"with":[14,150],"sparse":[15],"precision":[16,96,174],"matrices":[17,99,175],"using":[18],"a":[19,56,90,123,168,180,184,197],"Finite":[20],"Element":[21],"approximation":[22,63,92],"of":[23,41,49,100,105,122,135,179,191,203],"the":[24,47,95,101,136,155,173,189,201,208],"two-parameter":[25],"family,":[26],"\\[":[27],"(\u03ba^2":[28],"-":[29,139],"\u0394)^{\u03b1/2}":[30],"u":[31],"=":[32],"\\mathcal{W},":[33],"\\;\\;":[34],"\u03ba\\in":[35],"\\mathbb{R},":[36],"\\;":[37],"\u03b1\\in":[38],"\\mathbb{N}.":[39],"\\]":[40],"SPDEs.":[42],"Using":[43],"recent":[44],"developements":[45],"in":[46,167],"analysis":[48],"Discrete":[50],"Exterior":[51],"Calculus":[52],"(DEC),":[53],"we":[54,159],"present":[55],"different,":[57],"yet":[58],"closely":[59],"related,":[60],"convergent":[61,79,146],"GMRF":[62,209],"to":[64,84,188,206],"these":[65],"Mat\u00e9rn":[66,193],"over":[68,154],"complete,":[69],"boundaryless":[70],"Riemannian":[71],"manifolds":[72],"discretized":[73],"as":[74],"well-centered":[75],"simplicial":[76],"complexes.":[77],"This":[78],"method":[80],"(i)":[81],"is":[82,132],"agnostic":[83],"$\u03b1,":[85],"\u03ba$":[86],"and":[87,97,119,126,171,195],"thus":[88],"allows":[89],"universal":[91],"scheme":[93],"for":[94],"covariance":[98],"entire":[102],"$(\u03b1,":[103],"\u03ba)$-family":[104],"GMRFs,":[106],"so":[107],"they":[108],"may":[109],"be":[110],"inferred":[111],"rather":[112],"than":[113],"guessed.":[114],"(ii)":[115],"inherently":[116],"models":[117],"pointwise":[118],"piecewise-smoothed":[120],"measurements":[121,204],"random":[124],"field":[125],"approximates":[127],"both":[128],"equally":[129],"well":[130],"(iii)":[131],"computationally":[133],"independent":[134],"interpolants":[137],"used":[138],"it":[140],"suffers":[141],"no":[142],"overhead":[143],"if":[144],"one":[145],"interpolant":[147,153],"were":[148],"replaced":[149],"another":[151],"suitable":[152],"same":[156],"mesh.":[157],"Furthermore,":[158],"show":[160],"that,":[161],"on":[162],"discretizations":[163],"that":[164],"are":[165,176],"well-connected":[166],"precise":[169],"sense,":[170],"volume-concentrated,":[172],"spectral":[177],"functions":[178],"graph-laplacian.":[181],"We":[182],"provide":[183],"low":[185],"rank":[186],"approximator":[187],"family":[190],"such":[192],"GMRFs":[194],"mention":[196],"use":[198],"case:":[199],"reducing":[200],"number":[202],"needed":[205],"model":[207],"compressed-sensing.":[211]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-16T00:00:00"}
