Research On Algorithm And Application Of Multivariate Data Transform Approximation

Haar's theorem states the relationship between solvability of multivariate function interpolation and node group.According to the selection of node group and function application in multivariate function interpolation,it introduced the method of adding transformation,and then put forward the idea of data transformation:Starting from a given interpolation node group,it constructs appropriate data transformation,overcomes the limitations of traditional approximation,and makes some complex problems solvable and simplified.Directed by this idea,it proposed a bifurcation localization algorithm for optimal external axis of complex geometry and the application in medicine.The main part of dissertation is composed of three ones:The first part is about error analysis of function approximation,which mainly studied the error analysis of classical function interpolation.The estimation of truncated errors is significant for approximation methods,which concerns their convergence and precision.In this part,the interpolation remainder theorem and the truncated error formulas of Lagrange interpolation,Newton interpolation,Hermite interpolation,Piecewise linear interpolation,and cubic spline interpolation were concisely proved by mean value theorem for integrals,Rolle theorem and some specific inequalities.The second part is about the research of extraction the optimal external axisalgorithm.Firstly,K-means clustering was applied to optimize the search space,eliminate redundant computation,effectively sort out the search space,and reduce the possibility of particles falling into a local extremum.Then,by using the particle swarm optimization algorithm,it calculated the weight based on the distance of cluster center,initially generated particle swarm,and further improved the efficiency of the algorithm.Finally,it used a new adaptive method of inertia weight(NAIW)to adjust the inertia weight of particles,which improve the global search ability of particle swarm.The experimental results suggests that the algorithm is no longer less efficient of the optimal external axis traversal search.Compared with direct optimization algorithm,the average maximum acceleration ratio is 1288.67%,and the algorithm presents strong robustness.The third part proposed a special algorithm named bifurcation localization algorithm,and applied it to the field of medicine.First of all,according to a dataset,the 3D modelwere reconstructed by using 3D Slicer software and the particular area were extracted as well.Basing on the optimal external axis extraction method and bifurcation localization algorithm,it provided the precise position of puncture point and the best route during puncture and ablation of the intracranial hematoma operation.Finally,it generated threedimensional images fusion based on the brain and internal pathological areas of patients and related equipments during the operation.It has great significant guidance and value in formulating puncture operation plan and improving operation success rates.Figure 16;Table 4;Reference 63...