From 22e4fd76a13d86d8108eb96cc67388416738f846 Mon Sep 17 00:00:00 2001
From: SupZ <3321076758@qq.com>
Date: Tue, 28 May 2024 19:47:34 +0800
Subject: [PATCH] add
---
.gitignore | 29 +++
.idea/.gitignore | 8 +
.idea/dbnavigator.xml | 411 +++++++++++++++++++++++++++++++++
.idea/misc.xml | 6 +
.idea/modules.xml | 8 +
.idea/vcs.xml | 6 +
HomeWork_.iml | 11 +
src/LagrangeInterpolation.java | 30 +++
src/NewtonInterpolation.java | 46 ++++
src/T3.md | 9 +
10 files changed, 564 insertions(+)
create mode 100644 .gitignore
create mode 100644 .idea/.gitignore
create mode 100644 .idea/dbnavigator.xml
create mode 100644 .idea/misc.xml
create mode 100644 .idea/modules.xml
create mode 100644 .idea/vcs.xml
create mode 100644 HomeWork_.iml
create mode 100644 src/LagrangeInterpolation.java
create mode 100644 src/NewtonInterpolation.java
create mode 100644 src/T3.md
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..f68d109
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,29 @@
+### IntelliJ IDEA ###
+out/
+!**/src/main/**/out/
+!**/src/test/**/out/
+
+### Eclipse ###
+.apt_generated
+.classpath
+.factorypath
+.project
+.settings
+.springBeans
+.sts4-cache
+bin/
+!**/src/main/**/bin/
+!**/src/test/**/bin/
+
+### NetBeans ###
+/nbproject/private/
+/nbbuild/
+/dist/
+/nbdist/
+/.nb-gradle/
+
+### VS Code ###
+.vscode/
+
+### Mac OS ###
+.DS_Store
\ No newline at end of file
diff --git a/.idea/.gitignore b/.idea/.gitignore
new file mode 100644
index 0000000..13566b8
--- /dev/null
+++ b/.idea/.gitignore
@@ -0,0 +1,8 @@
+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml
diff --git a/.idea/dbnavigator.xml b/.idea/dbnavigator.xml
new file mode 100644
index 0000000..52282c8
--- /dev/null
+++ b/.idea/dbnavigator.xml
@@ -0,0 +1,411 @@
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\ No newline at end of file
diff --git a/.idea/misc.xml b/.idea/misc.xml
new file mode 100644
index 0000000..07115cd
--- /dev/null
+++ b/.idea/misc.xml
@@ -0,0 +1,6 @@
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\ No newline at end of file
diff --git a/.idea/modules.xml b/.idea/modules.xml
new file mode 100644
index 0000000..c70a0c6
--- /dev/null
+++ b/.idea/modules.xml
@@ -0,0 +1,8 @@
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\ No newline at end of file
diff --git a/.idea/vcs.xml b/.idea/vcs.xml
new file mode 100644
index 0000000..94a25f7
--- /dev/null
+++ b/.idea/vcs.xml
@@ -0,0 +1,6 @@
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\ No newline at end of file
diff --git a/HomeWork_.iml b/HomeWork_.iml
new file mode 100644
index 0000000..c90834f
--- /dev/null
+++ b/HomeWork_.iml
@@ -0,0 +1,11 @@
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\ No newline at end of file
diff --git a/src/LagrangeInterpolation.java b/src/LagrangeInterpolation.java
new file mode 100644
index 0000000..55f729f
--- /dev/null
+++ b/src/LagrangeInterpolation.java
@@ -0,0 +1,30 @@
+/**
+ * 第一题
+ */
+
+public class LagrangeInterpolation {
+ public static void main(String[] args) {
+ double[] t = {10, 15, 20, 22.5};
+ double[] v = {227.04, 362.78, 517.35, 602.97};
+
+ double targetT = 16;
+ double targetV = f1(t, v, targetT);
+ System.out.println(targetV);
+ }
+
+ public static double f1(double[] t, double[] v, double targetT) {
+ double result = 0.0;
+ int n = t.length;
+
+ for (int i = 0; i < n; i++) {
+ double term = v[i];
+ for (int j = 0; j < n; j++) {
+ if (i != j) {
+ term *= (targetT - t[j]) / (t[i] - t[j]);
+ }
+ }
+ result += term;
+ }
+ return result;
+ }
+}
diff --git a/src/NewtonInterpolation.java b/src/NewtonInterpolation.java
new file mode 100644
index 0000000..a0a5447
--- /dev/null
+++ b/src/NewtonInterpolation.java
@@ -0,0 +1,46 @@
+/**
+ * 第二题
+ */
+public class NewtonInterpolation {
+ public static void main(String[] args) {
+ // 定义时间点数组
+ double[] t = {10, 15, 20, 22.5};
+ // 定义速度值数组
+ double[] v = {227.04, 362.78, 517.35, 602.97};
+ // 目标时间点
+ double targetT = 16;
+ // 计算目标时间点的速度值
+ double targetV = f2(t, v, targetT);
+ // 输出结果
+ System.out.println(targetV);
+ }
+
+ // 牛顿插值法函数
+ public static double f2(double[] t, double[] v, double targetT) {
+ int n = t.length;
+ double[][] dividedDifference = new double[n][n];
+
+ // 初始化差商表第一列为给定速度值
+ for (int i = 0; i < n; i++) {
+ dividedDifference[i][0] = v[i];
+ }
+
+ // 计算差商表
+ for (int j = 1; j < n; j++) {
+ for (int i = 0; i < n - j; i++) {
+ dividedDifference[i][j] = (dividedDifference[i + 1][j - 1] - dividedDifference[i][j - 1]) / (t[i + j] - t[i]);
+ }
+ }
+
+ // 使用差商表计算插值多项式的值
+ double result = dividedDifference[0][0];
+ double term = 1.0;
+
+ // 构造插值多项式
+ for (int i = 1; i < n; i++) {
+ term *= (targetT - t[i - 1]);
+ result += dividedDifference[0][i] * term;
+ }
+ return result;
+ }
+}
diff --git a/src/T3.md b/src/T3.md
new file mode 100644
index 0000000..e04e82b
--- /dev/null
+++ b/src/T3.md
@@ -0,0 +1,9 @@
+# 第三题
+
+两种方法得到的结果相同。
+
+
+
+观点：
+
+在数据点很少的情况下，两种方法的精度没有区别
\ No newline at end of file