南京大学计算机科学与技术系：《数值计算方法》课程教学资源（PPT课件）第3章 解线性方程组的数值解法 3.1 高斯消元法

4.1 Lagrange插值法 4.2 Newton插值法

前面我们根据区间[ab]上给出的节点做 插值多项式Ln(x)近似表示f(x)。一般总 以为Ln(x)的次数越高,逼近f(x)的精度 越好,但实际并非如此,次数越高,计 算量越大,也不一定收敛。因此高次插 值一般要慎用,实际上较多采用分段低 次插值

略去余式R[f],由定理5.1.2知,它如果是插值型求积公式,则至少有n次代数精度

设矩阵A∈Rn,如果存在数入∈C及非零向量x∈C满足方程 Ax∈x,则称λ为矩阵A的一个特征值,称为矩阵A的相应于特 征值λ的特征向量。为简单起见,下称,x为矩阵A的一特征对。 特征值的计算,直接从特征方程()=det-A)=0出发会遇到很 大困难,当n稍大一些,行列式展开本身就很不容易,随后是高次代数 方程求解。因此,矩阵特征值的求解,主要是数值解法

2.1 Introduction: the role of packaging in the food chain Packaging has a significant role in the food supply chain and it is an integral part both of the food processes and the whole food supply chain. Food packaging has to perform several tasks as well as fulfilling many demands and requirements. Traditionally, a food package makes distribution easier. It has protected food from environmental conditions, such as light, oxygen, moisture, microbes, mechanical stresses and dust. Other basic tasks have been to ensure adequate labelling for providing information e.g., to the customer, and a proper convenience to the consumer, e.g., easy opening, reclosable lids and a suitable dosing mechanism. Basic requirements are good marketing properties

The best known and most widely used active packaging technologies for foods today are those engineered to remove undesirable substances from the headspace of a package through absorption, adsorption or scavenging. To achieve this goal a physical or chemical absorbent or adsorbent is incorporated in the packaging material or added to the package by means of a sachet. In most publications

5.1 Introduction Non-migratory bioactive polymers (NMBP)are a class of polymers that possess biological activity without the active components migrating from the polymer to the substrate. This concept has existed for some time (Bachler et al., 1970; Brody and Budny, 1995; Katchalski-Katzir 1993) and has been applied primarily to immobilised enzyme

As we know from the definition, intelligent or smart packaging monitors and gives information about the quality of the packed food. According to Huis in't give Veld (1996) the changes taking place in the fresh food product can be categorised as (i) microbiological growth and metabolism resulting in pH- changes, formation of toxic compounds off-odours, gas and slime formation

9.1 Introduction Drying is probably the oldest form of preservation Wrapping things that have been dried to protect them from moisture may well have been the earliest form of packaging. Even today a lot of technological development resources are expended to find new ways to package things to keep them dry. Some of the oldest materials used to control moisture are still used today: clay, salt, minerals and plant extracts that have a greater affinity for water than the material being protected. Clay has been used for centuries; moist clay to keep things moist and dried clay to keep things dry. Likewise the importance of salt is legendary