commit 22e4fd76a13d86d8108eb96cc67388416738f846
Author: SupZ <3321076758@qq.com>
Date: Tue May 28 19:47:34 2024 +0800
add
diff --git a/.gitignore b/.gitignore
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+### 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
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diff --git a/.idea/.gitignore b/.idea/.gitignore
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+# 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
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diff --git a/.idea/misc.xml b/.idea/misc.xml
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diff --git a/.idea/modules.xml b/.idea/modules.xml
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diff --git a/.idea/vcs.xml b/.idea/vcs.xml
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diff --git a/HomeWork_.iml b/HomeWork_.iml
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diff --git a/src/LagrangeInterpolation.java b/src/LagrangeInterpolation.java
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+++ b/src/LagrangeInterpolation.java
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+/**
+ * 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
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+/**
+ * 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
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+# 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
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