It is well known that many objects and problerns in mathematics or in mathematic physicshave property of periodicity. For example, in solving some differential equations intwo-dimensional domain, we can reduce them to...It is well known that many objects and problerns in mathematics or in mathematic physicshave property of periodicity. For example, in solving some differential equations intwo-dimensional domain, we can reduce them to periodic problems of various orthonormalwavelet bases in various spaces. In recent years, the study of periodic wavelets presentsactive tendency. For the purpose of varieties of applications, the author constructedthe periodic orthonormal quasi-wavelet bases in different spline spaces, for instanee, the pe-riodic polynomial spline functions, the spline functions on the circle (of complex展开更多
In solving integral equations with logarithmic kernel which arises from the boundary integral equation reformulation of some boundary value problems for the two dimensional Helmholtz equation, we combine the Galerkin ...In solving integral equations with logarithmic kernel which arises from the boundary integral equation reformulation of some boundary value problems for the two dimensional Helmholtz equation, we combine the Galerkin method with Beylkin's ([2]) approach, series of dense and nonsymmetric matrices may appear if we use traditional method. By appealing the so-called periodic quasi-wavelet (PQW in abbr.) ([5]), some of theme matrices become diagonal, therefore we can the a algorithm with only O(K(m)2) arithmetic operations where m is the highest level. The Galerkin approximation has a polynomial rate of convergence.展开更多
基金Project supported by the National Natural Science Foundation of China, and the Foundation of Zhongshan University Advanced Research Center.
文摘It is well known that many objects and problerns in mathematics or in mathematic physicshave property of periodicity. For example, in solving some differential equations intwo-dimensional domain, we can reduce them to periodic problems of various orthonormalwavelet bases in various spaces. In recent years, the study of periodic wavelets presentsactive tendency. For the purpose of varieties of applications, the author constructedthe periodic orthonormal quasi-wavelet bases in different spline spaces, for instanee, the pe-riodic polynomial spline functions, the spline functions on the circle (of complex
基金Partially supported by NNSFC and the Foundation of Zhongshan University Advanced ResearchCenter.
文摘In solving integral equations with logarithmic kernel which arises from the boundary integral equation reformulation of some boundary value problems for the two dimensional Helmholtz equation, we combine the Galerkin method with Beylkin's ([2]) approach, series of dense and nonsymmetric matrices may appear if we use traditional method. By appealing the so-called periodic quasi-wavelet (PQW in abbr.) ([5]), some of theme matrices become diagonal, therefore we can the a algorithm with only O(K(m)2) arithmetic operations where m is the highest level. The Galerkin approximation has a polynomial rate of convergence.
