Bit-complexity of classical solutions of linear evolutionary systems of partial differential equations

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dc.contributor.authorKoswara, Ivanko
dc.contributor.authorPogudin, Glebko
dc.contributor.authorSelivanova, Svetlanako
dc.contributor.authorZiegler, Martinko
dc.date.accessioned2023-04-10T09:00:46Z-
dc.date.available2023-04-10T09:00:46Z-
dc.date.created2023-04-10-
dc.date.created2023-04-10-
dc.date.issued2023-06-
dc.identifier.citationJOURNAL OF COMPLEXITY, v.76-
dc.identifier.issn0885-064X-
dc.identifier.urihttp://hdl.handle.net/10203/306087-
dc.description.abstractWe study the bit-complexity intrinsic to solving the initial-value and (several types of) boundary-value problems for linear evolu-tionary systems of partial differential equations (PDEs), based on the Computable Analysis approach. Our algorithms are guaranteed to compute classical solutions to such problems approximately up to error 1/2n, so that n corresponds to the number of reliable bits of the output; bit-cost is measured with respect to n. Computa-tional Complexity Theory allows us to prove in a rigorous sense that PDEs with constant coefficients are algorithmically 'easier' than general ones. Indeed, solutions to the latter are shown (un-der natural assumptions) computable using a polynomial number of memory bits, and we prove that the complexity class PSPACE is in general optimal; while the case of constant coefficients can be solved in #P-also essentially optimally so: the Heat Equation 're-quires' #P1. Our algorithms raise difference schemes to exponential powers, efficiently: we compute any desired entry of such a power in #P, provided that the underlying exponential-sized matrices are circulant of constant bandwidth. Exponentially powering modular two-band circulant matrices is established even feasible in P; and under additional conditions, also the solution to certain linear PDEs becomes polynomial time computable. (c) 2023 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.titleBit-complexity of classical solutions of linear evolutionary systems of partial differential equations-
dc.typeArticle-
dc.identifier.wosid000954986800001-
dc.identifier.scopusid2-s2.0-85148754256-
dc.type.rimsART-
dc.citation.volume76-
dc.citation.publicationnameJOURNAL OF COMPLEXITY-
dc.identifier.doi10.1016/j.jco.2022.101727-
dc.contributor.localauthorZiegler, Martin-
dc.contributor.nonIdAuthorKoswara, Ivan-
dc.contributor.nonIdAuthorPogudin, Gleb-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorReliable computing-
dc.subject.keywordAuthorBit-cost-
dc.subject.keywordAuthorPartial differential equations-
dc.subject.keywordAuthorPSPACE-
dc.subject.keywordPlusCOMPUTATIONAL-COMPLEXITY-
dc.subject.keywordPlusCOMPUTABILITY-
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