Abstract The goal of this study is to analyse the eigenvalues and weak eigenfunctions of a new type of multi-interval Sturm-Liouville problem (MISLP) which differs from the standard Sturm-Liouville problems (SLPs) in that the Strum-Liouville equation is defined on a finite number of non-intersecting subintervals and the boundary conditions are set not only at the endpoints but also at finite number internal points of interaction. For the self-adjoint treatment of the considered MISLP, we introduced some self-adjoint linear operators in such a way that the considered multi-interval SLPs can be interpreted as operator-pencil equation. First, we defined a concept of weak solutions (eigenfunctions) for MISLPs with interface conditions at the common ends of the subintervals. Then, we found some important properties of eigenvalues and corresponding weak eigenfunctions. In particular, we proved that the spectrum is discrete and the system of weak eigenfunctions forms a Riesz basis in appropriate Hilbert space.
{"title":"On completeness of weak eigenfunctions for multi-interval Sturm-Liouville equations with boundary-interface conditions","authors":"H. Olğar","doi":"10.1515/dema-2022-0210","DOIUrl":"https://doi.org/10.1515/dema-2022-0210","url":null,"abstract":"Abstract The goal of this study is to analyse the eigenvalues and weak eigenfunctions of a new type of multi-interval Sturm-Liouville problem (MISLP) which differs from the standard Sturm-Liouville problems (SLPs) in that the Strum-Liouville equation is defined on a finite number of non-intersecting subintervals and the boundary conditions are set not only at the endpoints but also at finite number internal points of interaction. For the self-adjoint treatment of the considered MISLP, we introduced some self-adjoint linear operators in such a way that the considered multi-interval SLPs can be interpreted as operator-pencil equation. First, we defined a concept of weak solutions (eigenfunctions) for MISLPs with interface conditions at the common ends of the subintervals. Then, we found some important properties of eigenvalues and corresponding weak eigenfunctions. In particular, we proved that the spectrum is discrete and the system of weak eigenfunctions forms a Riesz basis in appropriate Hilbert space.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49041957","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}
M. Vivas-Cortez, Maria Bibi, M. Muddassar, S. Al-Sa'di
Abstract Local fractional integral inequalities of Hermite-Hadamard type involving local fractional integral operators with Mittag-Leffler kernel have been previously studied for generalized convexities and preinvexities. In this article, we analyze Hermite-Hadamard-type local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) left({tilde{h}}_{1},{tilde{h}}_{2}) -preinvex function comprising local fractional integral operators and Mittag-Leffler kernel. In addition, two examples are discussed to ensure that the derived consequences are correct. As an application, we construct an inequality to establish central moments of a random variable.
摘要针对广义凸性和前凸性，研究了包含Mittag-Leffler核局部分数积分算子的Hermite-Hadamard型局部分数积分不等式。本文利用广义(h ～ 1, h ～ 2) left ({tilde{h}} ＿1, {}{tilde{h}} ＿2{) -预逆函数，利用Mittag-Leffler核和局部分数阶积分算子，分析了hermite - hadamard型局部分数阶积分不等式。此外，还讨论了两个例子，以确保推导的结果是正确的。作为一个应用，我们构造了一个不等式来建立一个随机变量的中心矩。}
{"title":"On local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) left({tilde{h}}_{1},{tilde{h}}_{2}) -preinvexity involving local fractional integral operators with Mittag-Leffler kernel","authors":"M. Vivas-Cortez, Maria Bibi, M. Muddassar, S. Al-Sa'di","doi":"10.1515/dema-2022-0216","DOIUrl":"https://doi.org/10.1515/dema-2022-0216","url":null,"abstract":"Abstract Local fractional integral inequalities of Hermite-Hadamard type involving local fractional integral operators with Mittag-Leffler kernel have been previously studied for generalized convexities and preinvexities. In this article, we analyze Hermite-Hadamard-type local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) left({tilde{h}}_{1},{tilde{h}}_{2}) -preinvex function comprising local fractional integral operators and Mittag-Leffler kernel. In addition, two examples are discussed to ensure that the derived consequences are correct. As an application, we construct an inequality to establish central moments of a random variable.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43511074","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}
Abstract In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We then prove the weak convergence theorem and present the numerical experiments for image recovery. The comparative results show that the proposed algorithm has better efficiency than other methods.
{"title":"New inertial forward–backward algorithm for convex minimization with applications","authors":"K. Kankam, W. Cholamjiak, P. Cholamjiak","doi":"10.1515/dema-2022-0188","DOIUrl":"https://doi.org/10.1515/dema-2022-0188","url":null,"abstract":"Abstract In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We then prove the weak convergence theorem and present the numerical experiments for image recovery. The comparative results show that the proposed algorithm has better efficiency than other methods.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46734314","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}
Choonkil Park, Mohammad Amin Tareeghee, Abbas Najati, Yavar Khedmati Yengejeh, Siriluk Paokanta
Abstract This article presents the general solution f:G→V f:{mathcal{G}}to {mathcal{V}} of the following functional equation: f(x)−4f(x+y)+6f(x+2y)−4f(x+3y)+f(x+4y)=0,x,y∈G, fleft(x)-4fleft(x+y)+6fleft(x+2y)-4fleft(x+3y)+fleft(x+4y)=0,hspace{1.0em}x,yin {mathcal{G}}, where (G,+) left({mathcal{G}},+) is an abelian group and V {mathcal{V}} is a linear space. We also investigate its Hyers-Ulam stability on some restricted domains. We apply the obtained results to present some asymptotic behaviors of this functional equation in the framework of normed spaces. Finally, we provide some characterizations of inner product spaces associated with the mentioned functional equation.
摘要本文给出了通解f: G→V f: { mathcal {G}} { mathcal {V}}以下函数方程:f (x)−4 f (x + y) + 6 f (x + 2 y)−4 f (x + 3 y) + f (x + 4) = 0, x, y∈G f 左(x) 4 f 左(x + y) + 6 f 离开(x + 2 y) 4 f 离开(x + 3 y) + f 离开(x + 4) = 0, 水平间距1.0 em} {x, y { mathcal {G}}, (G , + ) 左({ mathcal {G}}, +)是一个阿贝尔群和V { mathcal {V}}是一个线性空间。我们还研究了它在一些限制域上的Hyers-Ulam稳定性。利用所得结果，给出了该泛函方程在赋范空间框架下的一些渐近性质。最后，我们给出了与上述泛函方程相关的内积空间的一些表征。
{"title":"Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spaces","authors":"Choonkil Park, Mohammad Amin Tareeghee, Abbas Najati, Yavar Khedmati Yengejeh, Siriluk Paokanta","doi":"10.1515/dema-2023-0265","DOIUrl":"https://doi.org/10.1515/dema-2023-0265","url":null,"abstract":"Abstract This article presents the general solution <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> <m:mo>:</m:mo> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">G</m:mi> <m:mo>→</m:mo> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">V</m:mi> </m:math> f:{mathcal{G}}to {mathcal{V}} of the following functional equation: <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mn>6</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mn>3</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mn>4</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mspace width=\"1.0em\" /> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>y</m:mi> <m:mo>∈</m:mo> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">G</m:mi> <m:mo>,</m:mo> </m:math> fleft(x)-4fleft(x+y)+6fleft(x+2y)-4fleft(x+3y)+fleft(x+4y)=0,hspace{1.0em}x,yin {mathcal{G}}, where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">G</m:mi> <m:mo>,</m:mo> <m:mo>+</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> left({mathcal{G}},+) is an abelian group and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">V</m:mi> </m:math> {mathcal{V}} is a linear space. We also investigate its Hyers-Ulam stability on some restricted domains. We apply the obtained results to present some asymptotic behaviors of this functional equation in the framework of normed spaces. Finally, we provide some characterizations of inner product spaces associated with the mentioned functional equation.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262763","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}
Abstract In this article, an approximation of the image of the closed ball of the space L p {L}_{p} ( p > 1 pgt 1 ) centered at the origin with radius r r under Hilbert-Schmidt integral operator F ( ⋅ ) : L p → L q Fleft(cdot ):{L}_{p}to {L}_{q} , 1 p + 1 q = 1 frac{1}{p}+frac{1}{q}=1 is considered. An error evaluation for the given approximation is obtained.
摘要在本文中，空间Lp的闭球像的一个近似{L}_{p} Hilbert-Schmidt积分算子F（‧）：Lp→ L q Fleft（cdot）：{L}_{p} 到{L}_{q} ，1 p+1 q=1frac｛1｝｛p｝+frac{1｝{q｝=1。获得了给定近似的误差评估。
{"title":"Approximation of the image of the Lp ball under Hilbert-Schmidt integral operator","authors":"N. Huseyin","doi":"10.1515/dema-2022-0219","DOIUrl":"https://doi.org/10.1515/dema-2022-0219","url":null,"abstract":"Abstract In this article, an approximation of the image of the closed ball of the space L p {L}_{p} ( p > 1 pgt 1 ) centered at the origin with radius r r under Hilbert-Schmidt integral operator F ( ⋅ ) : L p → L q Fleft(cdot ):{L}_{p}to {L}_{q} , 1 p + 1 q = 1 frac{1}{p}+frac{1}{q}=1 is considered. An error evaluation for the given approximation is obtained.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43580821","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}
Abstract In this article, we discuss the existence of a unique solution to a ψ psi -Hilfer fractional differential equation involving the p p -Laplacian operator subject to nonlocal ψ psi -Riemann-Liouville fractional integral boundary conditions. Banach’s fixed point theorem is the main tool of our study. Examples are given for illustrating the obtained results.
摘要本文讨论了非局部ψ psi -Riemann-Liouville分数阶积分边界条件下包含p p - laplace算子的ψ psi -Hilfer分数阶微分方程的唯一解的存在性。巴拿赫不动点定理是我们研究的主要工具。给出了实例来说明所得结果。
{"title":"Uniqueness of solutions for a ψ-Hilfer fractional integral boundary value problem with the p-Laplacian operator","authors":"A. Alsaedi, M. Alghanmi, B. Ahmad, Boshra Alharbi","doi":"10.1515/dema-2022-0195","DOIUrl":"https://doi.org/10.1515/dema-2022-0195","url":null,"abstract":"Abstract In this article, we discuss the existence of a unique solution to a ψ psi -Hilfer fractional differential equation involving the p p -Laplacian operator subject to nonlocal ψ psi -Riemann-Liouville fractional integral boundary conditions. Banach’s fixed point theorem is the main tool of our study. Examples are given for illustrating the obtained results.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42501432","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}
Abstract The question of whether there is a true isometry approximating the ε varepsilon -isometry defined in the bounded subset of the n n -dimensional Euclidean space has long been considered an interesting question. In 1982, Fickett published the first article on this topic, and in early 2000, Alestalo et al. and Väisälä improved Fickett’s result significantly. Recently, the second author of this article published a paper improving the previous results. The main purpose of this article is to significantly improve all of the aforementioned results by applying a basic and intuitive method.
{"title":"Hyers-Ulam stability of isometries on bounded domains-II","authors":"Ginkyu Choi, Soon-Mo Jung","doi":"10.1515/dema-2022-0196","DOIUrl":"https://doi.org/10.1515/dema-2022-0196","url":null,"abstract":"Abstract The question of whether there is a true isometry approximating the ε varepsilon -isometry defined in the bounded subset of the n n -dimensional Euclidean space has long been considered an interesting question. In 1982, Fickett published the first article on this topic, and in early 2000, Alestalo et al. and Väisälä improved Fickett’s result significantly. Recently, the second author of this article published a paper improving the previous results. The main purpose of this article is to significantly improve all of the aforementioned results by applying a basic and intuitive method.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46318442","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}
Sivakumar Arundhathi, J. Alzabut, V. Muthulakshmi, Hakan Adıgüzel
Abstract In this study, we have investigated the oscillatory properties of the following fractional difference equation: ∇ α + 1 χ ( κ ) ⋅ ∇ α χ ( κ ) − p ( κ ) г ( ∇ α χ ( κ ) ) + q ( κ ) G ∑ μ = κ − α + 1 ∞ ( μ − κ − 1 ) ( − α ) χ ( μ ) = 0 , {nabla }^{alpha +1}chi left(kappa )cdot {nabla }^{alpha }chi left(kappa )-pleft(kappa )гleft({nabla }^{alpha }chi left(kappa ))+qleft(kappa ){mathcal{G}}left(mathop{sum }limits_{mu =kappa -alpha +1}^{infty }{left(mu -kappa -1)}^{left(-alpha )}chi left(mu )right)=0, where κ ∈ N 0 kappa in {{mathbb{N}}}_{0} , ∇ α {nabla }^{alpha } denotes the Liouville fractional difference operator of order α ∈ ( 0 , 1 ) alpha in left(0,1) , p p , and q q are nonnegative sequences, and г г and G {mathcal{G}} are real valued continuous functions, all of which satisfy certain assumptions. Using the generalized Riccati transformation technique, mathematical inequalities, and comparison results, we have found a number of new oscillation results. A few examples have been built up in this context to illustrate the main findings. The conclusion of this study is regarded as an expansion of continuous time to discrete time in fractional contexts.
{"title":"A certain class of fractional difference equations with damping: Oscillatory properties","authors":"Sivakumar Arundhathi, J. Alzabut, V. Muthulakshmi, Hakan Adıgüzel","doi":"10.1515/dema-2022-0236","DOIUrl":"https://doi.org/10.1515/dema-2022-0236","url":null,"abstract":"Abstract In this study, we have investigated the oscillatory properties of the following fractional difference equation: ∇ α + 1 χ ( κ ) ⋅ ∇ α χ ( κ ) − p ( κ ) г ( ∇ α χ ( κ ) ) + q ( κ ) G ∑ μ = κ − α + 1 ∞ ( μ − κ − 1 ) ( − α ) χ ( μ ) = 0 , {nabla }^{alpha +1}chi left(kappa )cdot {nabla }^{alpha }chi left(kappa )-pleft(kappa )гleft({nabla }^{alpha }chi left(kappa ))+qleft(kappa ){mathcal{G}}left(mathop{sum }limits_{mu =kappa -alpha +1}^{infty }{left(mu -kappa -1)}^{left(-alpha )}chi left(mu )right)=0, where κ ∈ N 0 kappa in {{mathbb{N}}}_{0} , ∇ α {nabla }^{alpha } denotes the Liouville fractional difference operator of order α ∈ ( 0 , 1 ) alpha in left(0,1) , p p , and q q are nonnegative sequences, and г г and G {mathcal{G}} are real valued continuous functions, all of which satisfy certain assumptions. Using the generalized Riccati transformation technique, mathematical inequalities, and comparison results, we have found a number of new oscillation results. A few examples have been built up in this context to illustrate the main findings. The conclusion of this study is regarded as an expansion of continuous time to discrete time in fractional contexts.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48733253","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}
Abstract In this article, we discuss equilibrium problems and their resolvents on complete geodesic spaces. In particular, we consider asymptotic behavior and continuity of resolvents with positive parameter in a complete geodesic space whose curvature is bounded above. Furthermore, we apply these results to resolvents of convex functions.
{"title":"Asymptotic behavior of resolvents of equilibrium problems on complete geodesic spaces","authors":"Y. Kimura, Keisuke Shindo","doi":"10.1515/dema-2022-0187","DOIUrl":"https://doi.org/10.1515/dema-2022-0187","url":null,"abstract":"Abstract In this article, we discuss equilibrium problems and their resolvents on complete geodesic spaces. In particular, we consider asymptotic behavior and continuity of resolvents with positive parameter in a complete geodesic space whose curvature is bounded above. Furthermore, we apply these results to resolvents of convex functions.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45236415","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}
Abstract In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.
{"title":"A dimension expanded preconditioning technique for block two-by-two linear equations","authors":"Wei-Hua Luo, Bruno Carpentieri, Jun Guo","doi":"10.1515/dema-2023-0260","DOIUrl":"https://doi.org/10.1515/dema-2023-0260","url":null,"abstract":"Abstract In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262933","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}
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