首页|Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

扫码查看
原文链接
  • 万方数据
  • 维普
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this work,we present a novel analysis tool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators.More precisely,for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations,we show that the associated quadratic form is positive definite under some easy-to-check algebraic conditions.Our proof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolution kernels and discrete complementary convolution kernels.To our knowledge,this is the first general result on simple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels.Using the unified theory,we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

discrete convolution kernelspositive definitenessvariable time-steppingorthogonal convolution kernelscomplementary convolution kernels

Hong-Lin Liao、Tao Tang、Tao Zhou

展开 >

School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China

Division of Science and Technology,BNU-HKBU United International College,Zhuhai 519087,China

SUSTech International Center for Mathematics,Shenzhen 518055,China

NCMIS & LSEC,Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

展开 >

National Natural Science Foundation of ChinaScience Challenge ProjectNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaYouth Innovation Promotion Association(CAS)Henan Academy of Sciencesreferees for their valuable comments

12071216TZ201800111731006K2091100112288201arXiv:2011.13383v1

2024

10.1007/s11425-022-2229-5

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(2)
  • 26