Mathematics of Computation最新文献

{"title":"Weak discrete maximum principle of isoparametric finite element methods in curvilinear polyhedra","authors":"Buyang Li, Weifeng Qiu, Yupei Xie, Wenshan Yu","doi":"10.1090/mcom/3876","DOIUrl":"https://doi.org/10.1090/mcom/3876","url":null,"abstract":"The weak maximum principle of the isoparametric finite element method is proved for the Poisson equation under the Dirichlet boundary condition in a (possibly concave) curvilinear polyhedral domain with edge openings smaller than <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi\"> <mml:semantics> <mml:mi>π<!-- π --></mml:mi> <mml:annotation encoding=\"application/x-tex\">pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which include smooth domains and smooth deformations of convex polyhedra. The proof relies on the analysis of a dual elliptic problem with a discontinuous coefficient matrix arising from the isoparametric finite elements. Therefore, the standard <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H squared\"> <mml:semantics> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">H^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> elliptic regularity which is required in the proof of the weak maximum principle in the literature does not hold for this dual problem. To overcome this difficulty, we have decomposed the solution into a smooth part and a nonsmooth part, and estimated the two parts by <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H squared\"> <mml:semantics> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">H^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper W Superscript 1 comma p\"> <mml:semantics> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">W^{1,p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> estimates, respectively. As an application of the weak maximum principle, we have proved a maximum-norm best approximation property of the isoparametric finite element method for the Poisson equation in a curvilinear polyhedron. The proof contains non-trivial modifications of Schatz’s argument due to the nonconformity of the iso-parametric finite elements, which requires us to construct a globally smooth flow map which maps the curvilinear polyhedron to a perturbed larger domain on which we can establish the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper W Superscript 1 comma normal infinity\"> <mml:semantics> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">W^{1,infty }<","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136383084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A monotone numerical flux for quasilinear convection diffusion equation","authors":"Claire Chainais-Hillairet, Robert Eymard, Jürgen Fuhrmann","doi":"10.1090/mcom/3870","DOIUrl":"https://doi.org/10.1090/mcom/3870","url":null,"abstract":"We propose a new numerical 2-point flux for a quasilinear convection–diffusion equation. This numerical flux is shown to be an approximation of the numerical flux derived from the solution of a two-point Dirichlet boundary value problem for the projection of the continuous flux onto the line connecting neighboring collocation points. The later approach generalizes an idea first proposed by Scharfetter and Gummel [IEEE Trans. Electron Devices <bold>16</bold> (1969), pp. 64–77] for linear drift-diffusion equations. We establish first that the new flux satisfies sufficient properties ensuring the convergence of the associate finite volume scheme, while respecting the maximum principle. Then, we pay attention to the long time behavior of the scheme: we show relative entropy decay properties satisfied by the new numerical flux as well as by the generalized Scharfetter-Gummel flux. The proof of these properties uses a generalization of some discrete (and continuous) log-Sobolev inequalities. The corresponding decay of the relative entropy of the continuous solution is proved in the appendix. Some 1D numerical experiments confirm the theoretical results.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135857716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial approximation of symmetric functions","authors":"Markus Bachmayr, Geneviève Dusson, Christoph Ortner","doi":"10.1090/mcom/3868","DOIUrl":"https://doi.org/10.1090/mcom/3868","url":null,"abstract":"We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f left-parenthesis x 1 comma ellipsis comma x Subscript upper N Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…<!-- … --></mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>N</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">f(x_1, dots , x_N)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x Subscript i Baseline element-of double-struck upper R Superscript d\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">x_i in mathbb {R}^d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is invariant under permutations of its <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=\"application/x-tex\">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> arguments. We demonstrate how these symmetries can be exploited to improve the cost versus error ratio in a polynomial approximation of the function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and in particular study the dependence of that ratio on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d comma upper N\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d, N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the polynomial degree. These results are then used to construct approximations and prove approximation rates for functions defined on multi-sets where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135210671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homomesies on permutations: An analysis of maps and statistics in the FindStat database","authors":"Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch","doi":"10.1090/mcom/3866","DOIUrl":"https://doi.org/10.1090/mcom/3866","url":null,"abstract":"In this paper, we perform a systematic study of permutation statistics and bijective maps on permutations in which we identify and prove 122 instances of the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on each orbit of a given map. The maps we investigate include the Lehmer code rotation, the reverse, the complement, the Foata bijection, and the Kreweras complement. The statistics studied relate to familiar notions such as inversions, descents, and permutation patterns, and also more obscure constructs. Besides the many new homomesy results, we discuss our research method, in which we used SageMath to search the FindStat combinatorial statistics database to identify potential homomesies.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136178677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Iterative solution of spatial network models by subspace decomposition","authors":"Morgan Görtz, Fredrik Hellman, Axel Målqvist","doi":"10.1090/mcom/3861","DOIUrl":"https://doi.org/10.1090/mcom/3861","url":null,"abstract":"We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be applied to a wide range of models, fulfilling a set of abstract assumptions. The proposed method builds on a classical subspace decomposition into a coarse subspace, realized as the restriction of a finite element space to the nodes of the spatial network, and localized subspaces with support on mesh stars. The main contribution of this work is the convergence analysis of the proposed method. The analysis translates results from finite element theory, including interpolation bounds, to the spatial network setting. A convergence rate of the PCG algorithm, only depending on global bounds of the operator and homogeneity, connectivity and locality constants of the network, is established. The theoretical results are confirmed by several numerical experiments.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135090628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability and convergence analysis of a fully discrete semi-implicit scheme for stochastic Allen-Cahn equations with multiplicative noise","authors":"Can Huang, Jie Shen","doi":"10.1090/mcom/3846","DOIUrl":"https://doi.org/10.1090/mcom/3846","url":null,"abstract":"We consider a fully discrete scheme for stochastic Allen-Cahn equation in a multi-dimensional setting. Our method uses a polynomial based spectral method in space, so it does not require the elliptic operator \u0000\u0000 \u0000 A\u0000 A\u0000 \u0000\u0000 and the covariance operator \u0000\u0000 \u0000 Q\u0000 Q\u0000 \u0000\u0000 of noise in the equation commute, and thus successfully alleviates a restriction of Fourier spectral method for stochastic partial differential equations pointed out by Jentzen, Kloeden and Winkel [Ann. Appl. Probab. 21 (2011), pp. 908–950]. The discretization in time is a tamed semi-implicit scheme which treats the nonlinear term explicitly while being unconditionally stable. Under regular assumptions which are usually made for SPDEs, we establish strong convergence rates in the one spatial dimension for our fully discrete scheme. We also present numerical experiments which are consistent with our theoretical results.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48263626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite element de Rham and Stokes complexes in three dimensions","authors":"Long Chen, Xuehai Huang","doi":"10.1090/mcom/3859","DOIUrl":"https://doi.org/10.1090/mcom/3859","url":null,"abstract":"Finite element de Rham complexes and finite element Stokes complexes with varying degrees of smoothness in three dimensions are systematically constructed in this paper. Smooth scalar finite elements in three dimensions are derived through a non-overlapping decomposition of the simplicial lattice. <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H left-parenthesis d i v right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>div</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">H(operatorname {div})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-conforming finite elements and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H left-parenthesis c u r l right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>curl</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">H(operatorname {curl})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-conforming finite elements with varying degrees of smoothness are devised based on these smooth scalar finite elements. The finite element de Rham complexes with corresponding smoothness and commutative diagrams are induced by these elements. The div stability of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H left-parenthesis d i v right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>div</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">H(operatorname {div})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-conforming finite elements is established, and the exactness of these finite element complexes is proven.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135363960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computing the spectral gap of a family of matrices","authors":"N. Guglielmi, V. Protasov","doi":"10.1090/mcom/3856","DOIUrl":"https://doi.org/10.1090/mcom/3856","url":null,"abstract":"For a single matrix (operator) it is well-known that the spectral gap is an important quantity, as well as its estimate and computation. Here we consider, for the first time in the literature, the computation of its extension to a finite family of matrices, in other words the difference between the joint spectral radius (in short JSR, which we call here the first Lyapunov exponent) and the second Lyapunov exponent (denoted as SLE). The knowledge of joint spectral characteristics and of the spectral gap of a family of matrices is important in several applications, as in the analysis of the regularity of wavelets, multiplicative matrix semigroups and the convergence speed in consensus algorithms. As far as we know the methods we propose are the first able to compute this quantity to any given accuracy.\u0000\u0000For computation of the spectral gap one needs first to compute the JSR. A popular tool that is used to this purpose is the invariant polytope algorithm, which relies on the finiteness property of the family of matrices, when this holds true.\u0000\u0000In this paper we show that the SLE may not possess the finiteness property, although it can be efficiently approximated with an arbitrary precision. The corresponding algorithm and two effective estimates are presented. Moreover, we prove that the SLE possesses a weak finiteness property, whenever the leading eigenvalue of the dominant product is real. This allows us to find in certain situations the precise value of the SLE. Numerical results are demonstrated along with applications in the theory of multiplicative matrix semigroups and in the wavelets theory.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48996200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility","authors":"Dianming Hou, Lili Ju, Zhonghua Qiao","doi":"10.1090/mcom/3843","DOIUrl":"https://doi.org/10.1090/mcom/3843","url":null,"abstract":"In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is carefully constructed based on the combination of first and second-order backward differentiation formulas with nonuniform time steps for temporal approximation and the central finite difference for spatial discretization. The discrete maximum bound principle is proved of the proposed scheme by using the kernel recombination technique under certain mild constraints on the time steps and the ratios of adjacent time step sizes. Furthermore, we rigorously derive the discrete <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H Superscript 1\"> <mml:semantics> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">H^{1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> error estimate and energy stability for the classic constant mobility case and the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript normal infinity\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^{infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> error estimate for the general mobility case. Various numerical experiments are also presented to validate the theoretical results and demonstrate the performance of the proposed method with a time adaptive strategy.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135812252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence analysis of the Halpern iteration with adaptive anchoring parameters","authors":"Songnian He, Hong-Kun Xu, Qiao-Li Dong, Na Mei","doi":"10.1090/mcom/3851","DOIUrl":"https://doi.org/10.1090/mcom/3851","url":null,"abstract":"We propose an adaptive way to choose the anchoring parameters for the Halpern iteration to find a fixed point of a nonexpansive mapping in a real Hilbert space. We prove strong convergence of this adaptive Halpern iteration and obtain the rate of asymptotic regularity at least <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis 1 slash k right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>1</mml:mn> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>k</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">O(1/k)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the number of iterations. Numerical experiments are also provided to show advantages and outperformance of our adaptive Halpern algorithm over the standard Halpern algorithm.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135812254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}