{"title":"Accurate Absorbing Boundary Conditions for the Two-Dimensional Nonlocal Schrödinger Equations","authors":"Gang Pang, Songsong Ji, Jiwei Zhang","doi":"10.1137/21m1442048","DOIUrl":"https://doi.org/10.1137/21m1442048","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89694382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Row Replicated Block Cimmino","authors":"I. Duff, P. Leleux, Daniel J. Ruiz, F. S. Torun","doi":"10.1137/22m1487710","DOIUrl":"https://doi.org/10.1137/22m1487710","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78800760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal-Order Convergence of a Two-Step BDF Method for the Navier-Stokes Equations with H1 Initial Data","authors":"Tianyang Chu, Jilu Wang, Nan Wang, Zhimin Zhang","doi":"10.1007/s10915-023-02270-x","DOIUrl":"https://doi.org/10.1007/s10915-023-02270-x","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"65 1","pages":"62"},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76268505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fast Computing Approaches Based on a Bilinear Pseudo-Spectral Method for Nonlinear Acoustic Wave Equations","authors":"M. Khasi, J. Rashidinia, M. Rasoulizadeh","doi":"10.1137/22m1506390","DOIUrl":"https://doi.org/10.1137/22m1506390","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87361995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A symmetrized parametric finite element method for anisotropic surface diffusion ii. three dimensions","authors":"W. Bao, Yifei Li","doi":"10.48550/arXiv.2206.01883","DOIUrl":"https://doi.org/10.48550/arXiv.2206.01883","url":null,"abstract":". For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy γ ( n ) in three dimensions (3D), where n is the unit outward normal vector, by introducing a novel symmetric positive definite surface energy matrix Z k ( n ) depending on a stabilizing function k ( n ) and the Cahn-Hoffman ξ -vector, we present a new symmetrized variational formulation for anisotropic surface diffusion with weakly or strongly anisotropic surface energy, which preserves two important structures including volume conservation and energy dissipation. Then we propose a structural-preserving parametric finite element method (SP-PFEM) to discretize the symmetrized variational problem, which preserves the volume in the discretized level. Under a relatively mild and simple condition on γ ( n ), we show that SP-PFEM is unconditionally energy- stable for almost all anisotropic surface energies γ ( n ) arising in practical applications. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as energy dissipation of the proposed SP-PFEM for solving anisotropic surface diffusion in 3D.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75516158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf, Mary Wootters
{"title":"Improved List Decoding of Folded Reed-Solomon and Multiplicity Codes","authors":"Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf, Mary Wootters","doi":"10.1137/20m1370215","DOIUrl":"https://doi.org/10.1137/20m1370215","url":null,"abstract":"We show new and improved list decoding properties of folded Reed-Solomon (RS) codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent advances in coding theory: Folded RS codes were the first known explicit construction of capacity-achieving list decodable codes (Guruswami and Rudra, IEEE Trans. Information Theory , 2010), and multiplicity codes were the first construction of high-rate locally decodable codes (Kopparty, Saraf, and Yekhanin, J. ACM , 2014). In this work, we show that folded RS codes and multiplicity codes are in fact better than was previously known in the context of list decoding and local list decoding. Our first main result shows that folded RS codes achieve list decoding capacity with constant list sizes, independent of the block length. Prior work with constant list sizes first obtained list sizes that are polynomial in the block length, and relied on pre-encoding with subspace evasive sets to reduce the list sizes to a constant (Guruswami and Wang, IEEE Trans. Information Theory , 2012; Dvir and Lovett, STOC , 2012). The list size we obtain is (1 /ε ) O (1 /ε ) where ε is the gap to capacity, which matches the list size obtained by pre-encoding with subspace evasive sets. For our second main result, we observe that univariate multiplicity codes exhibit similar behavior, and use this, together with additional ideas, to show that multivariate multiplicity codes are locally list decodable up to their minimum distance . By known reduc-tions, this gives in turn capacity-achieving locally list decodable codes with query complexity exp( ˜ O ((log N ) 5 / 6 )). This improves on the tensor-based construction of (Hemenway, Ron-Zewi, and Wootters, SICOMP , 2019), which gave capacity-achieving locally list decodable codes of query complexity","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"47 1","pages":"794-840"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85150634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Arnab Bhattacharyya, Sutanu Gayen, Eric Price, V. Tan, N. V. Vinodchandran
{"title":"Near-Optimal Learning of Tree-Structured Distributions by Chow and Liu","authors":"Arnab Bhattacharyya, Sutanu Gayen, Eric Price, V. Tan, N. V. Vinodchandran","doi":"10.1137/22m1489678","DOIUrl":"https://doi.org/10.1137/22m1489678","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"33 1","pages":"761-793"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73271043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}