# 数学代写|数值分析代写numerical analysis代考|CIVL2060

## 数学代写|数值分析代写numerical analysis代考|Other Properties of B-Splines

B-spline $B_{l v}$ forms a single partition as $$\sum_{v \in \mathbb{Z}} B_{l v}(x)=1, \quad x \in(-\infty, \infty)$$
Proof: If $l=0$, then, for every $x$ of $\left[x_v, x_{v+1}\right), B_{0 v}(x)=1$ and $B_{0, v}(x)=0$ on other intervals, then
$$\sum_{v \in \mathbb{Z}} B_{0 v}(x)=1$$
Now for $l \leq 1$, we can write $B_{l v}$ as follows:
$$B_{l v}(x)=q_l(\cdot, x)\left[t_{v+1}, \ldots, t_{v+l+1}\right]-q_l(\cdot, x)\left[t_v, \ldots, t_{v+l}\right]$$
So, we can conclude that for every $x$ of $\left[t_\mu, t_{\mu+1}\right]$, we have:
\begin{aligned} \sum_{v \in \mathbb{Z}} B_{l v}(x) &=\sum_{v=\mu-1}^\mu B_{l v}(x) \ &=\sum_{v=\mu-l}^\mu q_l(\cdot, x)\left[t_{v+1}, \ldots, t_{v+l+1}\right]-\sum_{v=\mu-1}^\mu q_l(\cdot, x)\left[t_v, \ldots, t_{v+l}\right] \ &=q_l(\cdot, x)\left[t_\mu, \ldots, t_{\mu+l+1}\right]-q_l(\cdot, x)\left[t_{\mu-l}, \ldots, t_\mu\right] \end{aligned}
The divided differences of the order $l$ with respect to $t$ from a polynomial $(t-x)^l$ is
$$q_l(\cdot, x)\left[t_{\mu+1}, \ldots, t_{\mu+l+1}\right]=1$$
which is the coefficient of the leading sentence, so its value is one. While for $x \in\left[t_\mu, t \mu+1\right], q_l(t, x)=(t, x){+}^l$ that $$q_l(\cdot, x)\left[t{\mu-1}, \ldots, t_\mu\right]=0, \quad t_{\mu-1, \ldots,}, t_\mu<x$$
Then,
$$\sum_{v \in \mathbb{Z}} B_{l v}(x)=1$$

## 数学代写|数值分析代写numerical analysis代考|Interval Interpolation

Sometimes the points used for interpolation may not be exactly available and we may have some parts of a data. For this type of data, the word “approximately” is commonly used. Now, if we want to make the word approximately and about meaningful, one of the ways is to use the interval, for example, we show about 2 with $[2-\varepsilon, 2+\varepsilon]$, where $\varepsilon$ is introduced arbitrarily. So, instead of about 2 or approximately 2, you can use a range that contains 2 . Classification of interval data is possible in two ways.

1. Data whose length and width are interval.
2. Data that only whose width is an interval.
Checking case (1) is more difficult than checking case (2). Because in case (1), the resulting interpolation criterion will have a complex and problematic form, so we will ignore it and only examine case (2). In this case, it is assumed that $n+1$ points are as follows:
$$\left(x_i,\left[f_i, \overline{f_i}\right]\right), \quad i=0, \ldots, n$$
If we want to consider the interpolation problem
$$\phi\left(x ; a_{0,}, \ldots, a_n\right)=\sum_{j=0}^n a_j \phi_j(x)$$
Such that the interpolation condition is satisfied, we have the following interval data
$$\phi\left(x ; a_0, \ldots, a_n\right)=\left[f_i, \bar{f}_i\right], \quad i=0, \ldots, n$$

# 数值分析代考

## 数学代写|数值分析代写numerical analysis代考|Other Properties of B-Splines

B样条 $B_{l v}$ 形成一个单一的分区
$$\sum_{v \in \mathbb{Z}} B_{l v}(x)=1, \quad x \in(-\infty, \infty)$$

$$\sum_{v \in \mathbb{Z}} B_{0 v}(x)=1$$

$$B_{l v}(x)=q_l(\cdot, x)\left[t_{v+1}, \ldots, t_{v+l+1}\right]-q_l(\cdot, x)\left[t_v, \ldots, t_{v+l}\right]$$

$$\sum_{v \in \mathbb{Z}} B_{l v}(x)=\sum_{v=\mu-1}^\mu B_{l v}(x) \quad=\sum_{v=\mu-l}^\mu q_l(\cdot, x)\left[t_{v+1}, \ldots, t_{v+l+1}\right]-\sum_{v=\mu-1}^\mu q_l(\cdot, x)\left[t_v, \ldots, t_{v+l}\right]=q_l(\cdot, x)$$

$$q_l(\cdot, x)\left[t_{\mu+1}, \ldots, t_{\mu+l+1}\right]=1$$

$$q_l(\cdot, x)\left[t \mu-1, \ldots, t_\mu\right]=0, \quad t_{\mu-1, \ldots,}, t_\mu<x$$

$$\sum_{v \in \mathbb{Z}} B_{l v}(x)=1$$

## 数学代写|数值分析代写numerical analysis代考|Interval Interpolation

1. 长宽为区间的数据。
2. 只有宽度为区间的数据。
检查案例 (1) 比检查案例 (2) 更难。因为在情况 (1) 中，得到的揷值准则将具有复杂且有问题的 形式，所以我们将忽略它，只检查情况（2）。在这种情况下，假设 $n+1$ 点如下: $\$ \$$Ifwewanttoconsidertheinterpolationproblem Suchthattheinterpolationconditionissatisfied, wehavethe followingintervaldata \ \$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: