The numerical differentiation of first and second order with tikhonov regularization 正則化方法求一階和兩階的數(shù)值微分
This thesis is to recommend a important class of regularized strategies for solving inverse problems - mollifier method . it anaysises the consistency , numerical stability and error estimates of mollified solution . similar to tikhonov regularization , a discrepancy principle for selecting the mol - lifier parameter is proven and applications to numerical differentiation and numerical inversion of abel transform and also given 本文將介紹求解反問(wèn)題的一類重要的正則化策略?緩鎮(zhèn)法,并基于用gauss核構(gòu)造的緩鎮(zhèn)算子,分析了緩鎮(zhèn)解的相容性、數(shù)值穩(wěn)定性和誤差估計(jì),與tikhonov正則化類似,我們證明了決定緩鎮(zhèn)參數(shù)的偏差原理。
Based on this ill - posed problem of edge detection , the edge types that exist in real images are described as mathematical models and the edge models that smoothed by gaussian function are regarded as the research objects . the paper systematically analyzes the characteristics of the different edge types and the relations between the localization of the different edge types and the smoothing scale while using the numerical differentiation as the method to detect edges 本文從邊緣檢測(cè)的“兩難”問(wèn)題出發(fā),對(duì)實(shí)際圖像中可能出現(xiàn)的邊緣類型進(jìn)行了數(shù)學(xué)模型描述,然后把高斯平滑后的邊緣模型作為研究對(duì)象,系統(tǒng)地分析了采用微分法檢測(cè)邊緣時(shí),不同的邊緣類型表現(xiàn)出來(lái)的特性,以及不同類型的邊緣定位與平滑尺度的關(guān)系。
百科解釋
In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.