Font Size: a A A

2D Interpolating Wavelets,Multifrequency Multifunctions Wavelets Nonharmonic Wavelets And Wavelets-Based Solutions To ODE

Posted on:2004-01-10Degree:DoctorType:Dissertation
Country:ChinaCandidate:Z ShiFull Text:PDF
GTID:1100360122480041Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
The results obtained in this dissertation include the following four aspects:(1) According to the theory of 2D Lagrangian interpolation, interpolating wavelets be researched. They have a number of desirable properties not possessed by wavelets of Daubechies type, namely: they have symmetry property; the scaling function and physical space representation are identical; expansion coefficients are easily computed; in certain respects they are more accurate; the functions (but not their derivatives) can be computed without solving an eigenproblem.The price to be paid for these advantages is the loss of orthogonality, interpolating wavelets are only Biorthogonal. For the type of computational problems we are concerned with ,however , the loss of orthogonality is unimportant.(2) In the study of multivariate phenomena, each time variable should possess its own scaling parameter in order to allow maximal flexibility in time-frequency. The notion of multifrequency multifunction wavelets, to be introduced, is based on this point of view. Multifrequency wavelets, via directional multiresolution analysis, generated by a single function is extended to multifrequency multifunction wavelets generated by a finite number of functions. Necessary and sufficient conditions for translates of the a finite number of functions form a orthogonality (or Riesz) basis forV0 are derived. The decomposition of wavelets generated by the finite number of functions is given.(3) Orthonormal wavelet basis be extended to nonharmonic wavelet basis ,m,n Z, . Byapplying the result to approximation function / which is " essentially localized " in time-frequency, we obtain good approximation effect.(4) As an application of wavelets, the first, wavelet-based solution to ODE to be researched, the second, construction the Hermite B-spline bases scale functions with boundary conditions on the interval, combining with Garlerkin method, to solve differential equation in finite-length beam problem; the third, M-scaling function solution to ODE in dynamics.
Keywords/Search Tags:2D interpolating wavelets, Multifrequency multifunction wavelets, Nonharmonic wavelet, Ordinary differential equation
PDF Full Text Request
Related items