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On zero behavior of higher-order Sobolev-type discrete $$q-$$ Hermite I orthogonal polynomials 论高阶索波列夫型离散 $$q-$$ 赫米特 I 正交多项式的零点行为
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-02 DOI: 10.1007/s11075-024-01868-y
Edmundo J. Huertas, Alberto Lastra, Anier Soria-Lorente, Víctor Soto-Larrosa
{"title":"On zero behavior of higher-order Sobolev-type discrete $$q-$$ Hermite I orthogonal polynomials","authors":"Edmundo J. Huertas, Alberto Lastra, Anier Soria-Lorente, Víctor Soto-Larrosa","doi":"10.1007/s11075-024-01868-y","DOIUrl":"https://doi.org/10.1007/s11075-024-01868-y","url":null,"abstract":"<p>In this work, we investigate the sequence of monic <i>q</i>-Hermite I-Sobolev type orthogonal polynomials of higher-order, denoted by <span>({mathbb {H}_{n}(x;q)}_{nge 0})</span>, which are orthogonal with respect to the following non-standard inner product involving <i>q</i>-differences: </p><span>$$begin{aligned} langle p,qrangle _{lambda }=int _{-1}^{1}fleft( xright) gleft( xright) (qx,-qx;q)_{infty }d_{q}(x)+lambda ,(mathscr {D}_{q}^{j}f)(alpha )(mathscr {D}_{q}^{j}g)(alpha ), end{aligned}$$</span><p>where <span>(lambda )</span> belongs to the set of positive real numbers, <span>(mathscr {D}_{q}^{j})</span> denotes the <i>j</i>-th <i>q</i> -discrete analogue of the derivative operator, <span>(q^jalpha in mathbb {R}backslash (-1,1))</span>, and <span>((qx,-qx;q)_{infty }d_{q}(x))</span> denotes the orthogonality weight with its points of increase in a geometric progression. Connection formulas between these polynomials and standard <i>q</i>-Hermite I polynomials are deduced. The basic hypergeometric representation of <span>(mathbb {H}_{n}(x;q))</span> is obtained. Moreover, for certain real values of <span>(alpha )</span> satisfying the condition <span>(q^jalpha in mathbb {R}backslash (-1,1))</span>, we present results concerning the location of the zeros of <span>(mathbb {H}_{n}(x;q))</span> and perform a comprehensive analysis of their asymptotic behavior as the parameter <span>(lambda )</span> tends to infinity.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"27 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient iterative procedures for approximating fixed points of contractive-type mappings with applications 近似收缩型映射定点的高效迭代程序及其应用
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-01 DOI: 10.1007/s11075-024-01869-x
Puneet Sharma, Higinio Ramos, Vinay Kanwar, Ramandeep Behl, Mithil Rajput
{"title":"Efficient iterative procedures for approximating fixed points of contractive-type mappings with applications","authors":"Puneet Sharma, Higinio Ramos, Vinay Kanwar, Ramandeep Behl, Mithil Rajput","doi":"10.1007/s11075-024-01869-x","DOIUrl":"https://doi.org/10.1007/s11075-024-01869-x","url":null,"abstract":"<p>This paper introduces and analyzes some new highly efficient iterative procedures for approximating fixed points of contractive-type mappings. The stability, data dependence, strong convergence, and performance of the proposed schemes are addressed. Numerical examples demonstrate that the newly introduced schemes produce approximations of great accuracy and comparable to other similar robust schemes appeared in the literature. Nevertheless, all the schemes developed here are more efficient than other robust schemes used for comparison.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"91 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The forward-backward-forward algorithm with extrapolation from the past and penalty scheme for solving monotone inclusion problems and applications 解决单调包含问题的前向-后向-前向算法与过去外推法和惩罚方案及其应用
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-28 DOI: 10.1007/s11075-024-01866-0
Buris Tongnoi
{"title":"The forward-backward-forward algorithm with extrapolation from the past and penalty scheme for solving monotone inclusion problems and applications","authors":"Buris Tongnoi","doi":"10.1007/s11075-024-01866-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01866-0","url":null,"abstract":"<p>In this paper, we consider an improved iterative method for solving the monotone inclusion problem in the form of <span>(0 in A(x) + D(x) + N_{C}(x))</span> in a real Hilbert space, where <i>A</i> is a maximally monotone operator, <i>D</i> and <i>B</i> are monotone and Lipschitz continuous, and <i>C</i> is the nonempty set of zeros of the operator <i>B</i>. We investigate the weak ergodic and strong convergence (when <i>A</i> is strongly monotone) of the iterates produced by our considered method. We show that the algorithmic scheme can also be applied to minimax problems. Furthermore, we discuss how to apply the method to the inclusion problem involving a finite sum of compositions of linear continuous operators by using the product space approach and employ it for convex minimization. Finally, we present a numerical experiment in TV-based image inpainting to validate the proposed theoretical theorem.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"122 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence rate and exponential stability of backward Euler method for neutral stochastic delay differential equations under generalized monotonicity conditions 广义单调性条件下中性随机延迟微分方程的后向欧拉法收敛率和指数稳定性
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-28 DOI: 10.1007/s11075-024-01862-4
Jingjing Cai, Ziheng Chen, Yuanling Niu
{"title":"Convergence rate and exponential stability of backward Euler method for neutral stochastic delay differential equations under generalized monotonicity conditions","authors":"Jingjing Cai, Ziheng Chen, Yuanling Niu","doi":"10.1007/s11075-024-01862-4","DOIUrl":"https://doi.org/10.1007/s11075-024-01862-4","url":null,"abstract":"<p>This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect to both delay variables and state variables. Under generalized monotonicity conditions, we prove that the backward Euler method not only converges strongly in the mean square sense with order 1/2, but also inherit the mean square exponential stability of the original equations. As a byproduct, we obtain the same results on convergence rate and exponential stability of the backward Euler method for stochastic delay differential equations under generalized monotonicity conditions. These theoretical results are finally supported by several numerical experiments.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"86 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fast second-order absorbing boundary condition for the linearized Benjamin-Bona-Mahony equation 线性化本杰明-博纳-马霍尼方程的快速二阶吸收边界条件
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-26 DOI: 10.1007/s11075-024-01864-2
Zijun Zheng, Gang Pang, Matthias Ehrhardt, Baiyili Liu
{"title":"A fast second-order absorbing boundary condition for the linearized Benjamin-Bona-Mahony equation","authors":"Zijun Zheng, Gang Pang, Matthias Ehrhardt, Baiyili Liu","doi":"10.1007/s11075-024-01864-2","DOIUrl":"https://doi.org/10.1007/s11075-024-01864-2","url":null,"abstract":"<p>In this paper, we present a fully discrete finite difference scheme with efficient convolution of artificial boundary conditions for solving the Cauchy problem associated with the one-dimensional linearized Benjamin-Bona-Mahony equation. The scheme utilizes the Padé expansion of the square root function in the complex plane to implement the fast convolution, resulting in significant reduction of computational costs involved in the time convolution process. Moreover, the introduction of a constant damping term in the governing equations allows for convergence analysis under specific conditions. The theoretical analysis is complemented by numerical examples that illustrate the performance of the proposed numerical method.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"27 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A reliable numerical algorithm mixed with hypergeometric function for analyzing fractional variational problems 用于分析分数变分问题的混合超几何函数的可靠数值算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-25 DOI: 10.1007/s11075-024-01865-1
Z. Zarvan, K. Sayevand, R. M. Ganji, H. Jafari
{"title":"A reliable numerical algorithm mixed with hypergeometric function for analyzing fractional variational problems","authors":"Z. Zarvan, K. Sayevand, R. M. Ganji, H. Jafari","doi":"10.1007/s11075-024-01865-1","DOIUrl":"https://doi.org/10.1007/s11075-024-01865-1","url":null,"abstract":"<p>The present study aims to introduce a numerical approach based on the hybrid of block-pulse functions (BPFs), Bernoulli polynomials (BPs), and hypergeometric function for analyzing a class of fractional variational problems (FVPs). The FVPs are made by the Caputo derivative sense. To analyze this problem, first, we create an approximate for the Riemann-Liouville fractional integral operator for BPFs and BPs of the fractional order. In this framework and using the Gauss-Legendre points, the main problem is converted into a system of algebraic equations. In the follow-up, an accurate upper bound is obtained and some theorems are established on the convergence analysis. Moreover, the computational order of convergence and solvability of the proposed approach are displayed and approximated theoretically and numerically. Meanwhile, the thrust of the proposed scheme is compared with other sophisticated examples in the literature, demonstrating that the process is accurate and efficient.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
General double-relaxation two-sweep modulus-based matrix splitting iteration methods for horizontal linear complementarity problem 针对水平线性互补问题的基于模数的通用双松弛两扫矩阵分割迭代法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-25 DOI: 10.1007/s11075-024-01860-6
Dan Wang, Jicheng Li
{"title":"General double-relaxation two-sweep modulus-based matrix splitting iteration methods for horizontal linear complementarity problem","authors":"Dan Wang, Jicheng Li","doi":"10.1007/s11075-024-01860-6","DOIUrl":"https://doi.org/10.1007/s11075-024-01860-6","url":null,"abstract":"<p>For solving horizontal linear complementarity problem (HLCP), we propose a general double-relaxation two-sweep modulus-based matrix splitting iteration method and a double-relaxation two-sweep modulus-based matrix splitting iteration method which contain a series of methods, by using different splittings. When the system matrices are <span>(H_+)</span>-matrices, we analyze convergence theory of these methods. Numerical examples in this paper illustrate that these methods are more efficient than modulus-based matrix splitting iteration method and general modulus-based matrix splitting iteration method.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"222 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral characterizations and integer powers of tridiagonal 2-Toeplitz matrices 三对角 2-Toeplitz 矩阵的谱特征和整数幂
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-22 DOI: 10.1007/s11075-024-01863-3
Maryam Shams Solary, Stefano Serra-Capizzano
{"title":"Spectral characterizations and integer powers of tridiagonal 2-Toeplitz matrices","authors":"Maryam Shams Solary, Stefano Serra-Capizzano","doi":"10.1007/s11075-024-01863-3","DOIUrl":"https://doi.org/10.1007/s11075-024-01863-3","url":null,"abstract":"<p>In this note, we consider real nonsymmetric tridiagonal 2-Toeplitz matrices <span>(textbf{B}_n)</span>. First we give the asymptotic spectral and singular value distribution of the whole matrix-sequence <span>({textbf{B}_n}_n)</span>, which is described via two eigenvalue functions of a <span>(2times 2)</span> matrix-valued symbol. In connection with the above findings, we provide a characterization of the eigenvalues and eigenvectors of real tridiagonal 2-Toeplitz matrices <span>(textbf{B}_n)</span> of even order, that can be turned into a numerical effective scheme for the computation of all the entries of <span>(textbf{B}_n^l)</span>, <i>n</i> even and <i>l</i> positive and small compared to <i>n</i>. We recall that a corresponding eigenvalue decomposition for odd order tridiagonal 2-Toeplitz matrices was found previously, while, for even orders, an implicit formula for all the eigenvalues is obtained.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"193 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence analysis of Picard–SP iteration process for generalized $$alpha $$ –nonexpansive mappings 广义$$alpha$$无穷映射的Picard-SP迭代过程收敛性分析
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-18 DOI: 10.1007/s11075-024-01859-z
Bashir Nawaz, Kifayat Ullah, Krzysztof Gdawiec
{"title":"Convergence analysis of Picard–SP iteration process for generalized $$alpha $$ –nonexpansive mappings","authors":"Bashir Nawaz, Kifayat Ullah, Krzysztof Gdawiec","doi":"10.1007/s11075-024-01859-z","DOIUrl":"https://doi.org/10.1007/s11075-024-01859-z","url":null,"abstract":"<p>In this manuscript, we introduce a novel hybrid iteration process called the Picard–SP iteration process. We apply this new iteration process to approximate fixed points of generalized <span>(alpha )</span>–nonexpansive mappings. Convergence analysis of our newly proposed iteration process is discussed in the setting of uniformly convex Banach spaces and results are correlated with some other existing iteration processes. The dominance of the newly proposed iteration process is exhibited with the help of a new numerical example. In the end, the comparison of polynomiographs generated by other well-known iteration processes with our proposed iteration process has been presented to make a strong impression of our proposed iteration process.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$$L^2$$ norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations 不可压缩纳维-斯托克斯方程的变步长 IMEX BDF2 方案的 $L^2$$ 规范收敛性
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-17 DOI: 10.1007/s11075-024-01858-0
Bingquan Ji, Xuan Zhao
{"title":"$$L^2$$ norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations","authors":"Bingquan Ji, Xuan Zhao","doi":"10.1007/s11075-024-01858-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01858-0","url":null,"abstract":"<p>We present an <span>(L^2)</span> norm convergence of the implicit-explicit BDF2 scheme with variable-step for the unsteady incompressible Navier-Stokes equations with an inf-sup stable FEM for the space discretization. Under a weak step-ratio constraint <span>(0&lt;r_k:=tau _k/tau _{k-1}&lt;4.864)</span>, our error estimate is mesh-robust in the sense that it completely removes the possibly unbounded quantities, such as <span>(Gamma _N=sum _{k=1}^{N-2}max {0,r_{k}-r_{k+2}})</span> and <span>(Lambda _N=sum _{k=1}^{N-1}(|r_{k}-1|+|r_{k+1}-1|))</span> included in previous studies. In this analysis, we integrate our recent theoretical framework that employs discrete orthogonal convolution (DOC) kernels with an auxiliary Stokes problem to split the convergence analysis into two distinct parts. In the first part, we address intricate consistency error estimates for the velocity, pressure and nonlinear convection term. The resulting estimates allow us to utilize the conventional methodologies within the DOC framework to preserve spatial accuracy. In the second part, through the use of the DOC technique, we prove that the proposed variable-step BDF2 scheme is of second-order accuracy in time with respect to the <span>(L^2)</span> norm. Extensive numerical simulations coupled with an adaptive time-stepping algorithm are performed to show the accuracy and efficiency of the proposed variable-step method for the incompressible flows.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"16 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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