Horner算法和Muller算法完成。

Author: computeone

CNumericalCalculation.vcxproj

@@ -78,13 +78,19 @@
   <ItemGroup>
     <ClInclude Include="BinaryDivide.h" />
     <ClInclude Include="FixedIterator.h" />
+    <ClInclude Include="Horner.h" />
+    <ClInclude Include="Interpolation.h" />
     <ClInclude Include="NewTonIterator.h" />
+    <ClInclude Include="Steffensen.h" />
   </ItemGroup>
   <ItemGroup>
     <ClCompile Include="BinaryDivide.cpp" />
     <ClCompile Include="FixedIterator.cpp" />
+    <ClCompile Include="Horner.cpp" />
+    <ClCompile Include="Interpolation.cpp" />
     <ClCompile Include="main.cpp" />
     <ClCompile Include="NewTonIterator.cpp" />
+    <ClCompile Include="Steffensen.cpp" />
   </ItemGroup>
   <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
   <ImportGroup Label="ExtensionTargets">

CNumericalCalculation.vcxproj.filters

@@ -24,6 +24,15 @@
     <ClInclude Include="NewTonIterator.h">
       <Filter>头文件</Filter>
     </ClInclude>
+    <ClInclude Include="Steffensen.h">
+      <Filter>头文件</Filter>
+    </ClInclude>
+    <ClInclude Include="Horner.h">
+      <Filter>头文件</Filter>
+    </ClInclude>
+    <ClInclude Include="Interpolation.h">
+      <Filter>头文件</Filter>
+    </ClInclude>
   </ItemGroup>
   <ItemGroup>
     <ClCompile Include="BinaryDivide.cpp">
@@ -38,5 +47,14 @@
     <ClCompile Include="NewTonIterator.cpp">
       <Filter>源文件</Filter>
     </ClCompile>
+    <ClCompile Include="Steffensen.cpp">
+      <Filter>源文件</Filter>
+    </ClCompile>
+    <ClCompile Include="Horner.cpp">
+      <Filter>源文件</Filter>
+    </ClCompile>
+    <ClCompile Include="Interpolation.cpp">
+      <Filter>源文件</Filter>
+    </ClCompile>
   </ItemGroup>
 </Project>

Debug/BinaryDivide.obj

@@ -0,0 +1,15 @@
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\vc120.pdb
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\vc120.idb
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\binarydivide.obj
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\main.obj
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\fixediterator.obj
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\newtoniterator.obj
+d:\c++\workspace\sunsystem\debug\cnumericalcalculation.ilk
+d:\c++\workspace\sunsystem\debug\cnumericalcalculation.exe
+d:\c++\workspace\sunsystem\debug\cnumericalcalculation.pdb
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\cnumeric.7d3823d4.tlog\cl.command.1.tlog
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\cnumeric.7d3823d4.tlog\cl.read.1.tlog
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\cnumeric.7d3823d4.tlog\cl.write.1.tlog
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\cnumeric.7d3823d4.tlog\link.command.1.tlog
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\cnumeric.7d3823d4.tlog\link.read.1.tlog
+d:\c++\workspace\sunsystem\cnumericalcalculation\debug\cnumeric.7d3823d4.tlog\link.write.1.tlog

Debug/CNumeric.7D3823D4.tlog/CL.read.1.tlog

@@ -1,24 +1,26 @@
-生成启动时间为 4/6/2014 8:11:34 PM。
+生成启动时间为 4/14/2014 9:18:22 PM。
      1>项目“D:\C++\WorkSpace\SunSystem\CNumericalCalculation\CNumericalCalculation.vcxproj”在节点 2 上(Build 个目标)。
      1>ClCompile:
-         D:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin\CL.exe /c /ZI /nologo /W3 /WX- /Od /Oy- /D WIN32 /D _DEBUG /D _CONSOLE /D _LIB /D _UNICODE /D UNICODE /Gm /EHsc /RTC1 /MDd /GS /fp:precise /Zc:wchar_t /Zc:forScope /Fo"Debug\\" /Fd"Debug\vc120.pdb" /Gd /TP /analyze- /errorReport:prompt NewTonIterator.cpp main.cpp
+         D:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin\CL.exe /c /ZI /nologo /W3 /WX- /Od /Oy- /D WIN32 /D _DEBUG /D _CONSOLE /D _LIB /D _UNICODE /D UNICODE /Gm /EHsc /RTC1 /MDd /GS /fp:precise /Zc:wchar_t /Zc:forScope /Fo"Debug\\" /Fd"Debug\vc120.pdb" /Gd /TP /analyze- /errorReport:prompt Horner.cpp main.cpp
          main.cpp
-     1>d:\c++\workspace\sunsystem\cnumericalcalculation\main.cpp(10): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
-         NewTonIterator.cpp
-     1>d:\c++\workspace\sunsystem\cnumericalcalculation\newtoniterator.cpp(6): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
-     1>d:\c++\workspace\sunsystem\cnumericalcalculation\newtoniterator.cpp(7): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
-     1>d:\c++\workspace\sunsystem\cnumericalcalculation\newtoniterator.cpp(23): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
+     1>d:\c++\workspace\sunsystem\cnumericalcalculation\main.cpp(12): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
+         Horner.cpp
+     1>d:\c++\workspace\sunsystem\cnumericalcalculation\horner.cpp(37): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
+     1>d:\c++\workspace\sunsystem\cnumericalcalculation\horner.cpp(53): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
+     1>d:\c++\workspace\sunsystem\cnumericalcalculation\horner.cpp(55): warning C4244: “参数”: 从“double”转换到“float”，可能丢失数据
          正在生成代码...
-     1>d:\c++\workspace\sunsystem\cnumericalcalculation\newtoniterator.cpp(27): warning C4715: “NewTonIterator”: 不是所有的控件路径都返回值
-     1>d:\c++\workspace\sunsystem\cnumericalcalculation\newtoniterator.cpp(48): warning C4715: “NewTonIterator”: 不是所有的控件路径都返回值
+     1>d:\c++\workspace\sunsystem\cnumericalcalculation\horner.cpp(80): warning C4715: “Muller”: 不是所有的控件路径都返回值
        Link:
          D:\Program Files (x86)\Microsoft Visual Studio 12.0\VC\bin\link.exe /ERRORREPORT:PROMPT /OUT:"D:\C++\WorkSpace\SunSystem\Debug\CNumericalCalculation.exe" /INCREMENTAL /NOLOGO kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib /MANIFEST /MANIFESTUAC:"level='asInvoker' uiAccess='false'" /manifest:embed /DEBUG /PDB:"D:\C++\WorkSpace\SunSystem\Debug\CNumericalCalculation.pdb" /SUBSYSTEM:CONSOLE /TLBID:1 /DYNAMICBASE /NXCOMPAT /IMPLIB:"D:\C++\WorkSpace\SunSystem\Debug\CNumericalCalculation.lib" /MACHINE:X86 Debug\BinaryDivide.obj
          Debug\FixedIterator.obj
+         Debug\Horner.obj
+         Debug\Interpolation.obj
          Debug\main.obj
          Debug\NewTonIterator.obj
+         Debug\Steffensen.obj
          CNumericalCalculation.vcxproj -> D:\C++\WorkSpace\SunSystem\Debug\CNumericalCalculation.exe
      1>已完成生成项目“D:\C++\WorkSpace\SunSystem\CNumericalCalculation\CNumericalCalculation.vcxproj”(Build 个目标)的操作。
 
 生成成功。
 
-已用时间 00:00:02.24
+已用时间 00:00:02.26

Debug/CNumeric.7D3823D4.tlog/CL.write.1.tlog

@@ -31,7 +31,7 @@ double fixedIterator(double p0, double tol,int N, double(*function)(double p)){
 		p = function(p0);
 		cout << setprecision(16)<<"p:" << endl << endl;
 		if (fabs(p - p0) < tol){
-			cout << "不 动点迭代结束：" << endl;
+			cout << "不动点迭代结束：" << endl;
 		}
 		p0 = p;
 	}

Debug/CNumeric.7D3823D4.tlog/cl.command.1.tlog

@@ -0,0 +1,80 @@
+#include "Horner.h"
+#include <iostream>
+
+using namespace std;
+
+
+pair<double,double> Horner(double x0){
+	double a[5];
+	a[4] = 2;
+	a[3] = 0;
+	a[2] = -3;
+	a[1] = 3;
+	a[0] = -4;
+
+	double y = a[4];
+	double z = a[4];
+	for (int j = 1; j < 4; j++){
+		y = x0*y + a[4 - j];
+		z = x0*z + y; 
+	}
+	y = x0*y + a[0];	
+	return pair<double,double>(y,z);
+}
+
+pair<double,double> Horner(double x0,int n,double a[], double(*function)(double)){
+	double y = a[n - 1];
+	double z = a[n - 1];
+	for (int j = 1; j < n - 1; j++){
+		y = x0*y + a[n - 1 - j];
+		z = x0*z + y;
+	}
+	y = x0*y + a[0];
+	return pair<double,double>(y,z);
+}
+
+double testMuller(double x){
+	return 16 * powf(x, 4) - 40 * powf(x, 3) + 5 * powf(x, 2) + 20 * x + 6;
+}
+double Muller(double x0, double x1, double x2, double tol, int n, double(*function)(double)){
+
+	double h1 = x1 - x0;
+	double h2 = x2 - x1;
+	double p1 = (function(x1) - function(x0)) / h1;
+	double p2 = (function(x2) - function(x1)) / h2;
+	double d = (p2 - p1) / (h2 + h1);
+	cout << d << endl;
+	int i = 3;
+	cout << "Muller算法开始：" << endl;
+	while (i <= n){
+		double b = p2 + h2*d;
+
+		//可能复数运算
+		double D = sqrtf(powf(b, 2) - 4 * function(x2)*d);
+		double E;
+		if (fabsf(b - D) < fabsf(b + D)){
+			E = b + D;
+		}
+		else{
+			E = b - D;
+		}
+		double h = -2 * function(x2) / E;
+		double p = x2 + h;
+		cout << "p:" << p << endl;
+		if (fabs(h) < tol){
+			cout << "Muller算法结束!" << endl;
+			return p;
+		}
+		//设置下一次迭代
+		x0 = x1;
+		x1 = x2;
+		x2 = p;
+		h1 = x1 - x0;
+		h2 = x2 - x1;
+		p1 = (function(x1) - function(x0)) / h1;
+		p2 = (function(x2) - function(x1)) / h2;
+		d = (p2 - p1) / (h2 + h1);
+		i = i + 1;
+	}
+	cout << "Muller算法失败！" << endl;
+}

Debug/CNumeric.7D3823D4.tlog/link.command.1.tlog

@@ -0,0 +1,13 @@
+#include <iostream>
+
+using namespace std;;
+
+
+//Horner算法，求多项式p(x)=AnX^n+An-1X^n-1+....a1X+a0=(x-x0)Q(x)+b0的值和导数
+
+pair<double,double> Horner(double x0);
+pair<double,double> Horner(double x0, int n,double a[],double(*function)(double));
+
+double testMuller(double x);
+// Muller算法，求多项式的m重根
+double Muller(double x0, double x1, double x2, double tol, int n, double(*function)(double));

Debug/CNumeric.7D3823D4.tlog/link.read.1.tlog

@@ -0,0 +1,4 @@
+#include "Interpolation.h"
+#include <iostream>
+
+using namespace std;

Debug/CNumeric.7D3823D4.tlog/link.write.1.tlog

@@ -0,0 +1,8 @@
+#include <iostream>
+
+using namespace std;
+
+/*
+²åÖµÓë¶àÏîʽ±Æ½ü
+*/
+

Debug/CNumericalCalculation.Build.CppClean.log

@@ -0,0 +1,43 @@
+#include "Steffensen.h"
+#include <iostream>
+
+double Steffensen(double p0, double tol, int n){
+	int i = 1;
+	double p1, p2,p;
+	cout << "Steffense快速收敛算法开始：" << endl;
+	while (i <= n){
+		p1 = sqrtf(10/(p0+4));
+		p2 = sqrtf(10/(p1+4));
+		p = p0 - powf(p1 - p0, 2) / (p2 - 2 * p1 + p0);
+		cout << "p:" << p << endl;
+		if (fabs(p - p0) < tol){
+			cout << "Steffense快速收敛算法结束:" << endl;
+			return p;
+		}
+		i += 1;
+		p0 = p;
+	}
+	cout << "Stenffense快速收敛算法失败！" << endl;
+	return NULL;
+}
+
+double Steffensen(double p0, double tol, int n, double(*function)(double)){
+	int i = 1;
+	double p1, p2, p;
+	cout << "Steffense快速收敛算法开始：" << endl;
+	while (i <= n){
+		p1 = function(p0);
+		p2 = function(p1);
+		p = p0 - powf(p1 - p0, 2) / (p2 - 2 * p1 + p0);
+		cout << "p:" << p << endl;
+		if (fabsf(p - p0) < tol){
+			cout << "Steffense快速收敛算法结束:" << endl;
+			return p;
+		}
+		i = i + 1;
+		p0 = p;
+	}
+
+	cout << "Stenffense快速收敛算法失败！" << endl;
+	return NULL;
+}

Debug/CNumericalCalculation.log

@@ -0,0 +1,8 @@
+#include <iostream>
+
+using namespace std;
+
+
+//Steffensen方法是具有二次收敛速度的算法,不动点迭代算法改进性
+double Steffensen(double p0, double tol, int N);
+double Steffensen(double p0, double tol, int N, double(*function)(double));

Debug/FixedIterator.obj

@@ -1,6 +1,8 @@
 #include "BinaryDivide.h"
 #include "FixedIterator.h"
 #include "NewTonIterator.h"
+#include "Steffensen.h"
+#include "Horner.h"
 #include <iostream>
 #include <algorithm>
 
@@ -19,8 +21,17 @@ void testFixedIterator(){
 void testNewTonIterator(){
 	cout << "根为:" << NewTonIterator(0.5, 3.1415926/4.0,0.000001,10,test) << endl;
 }
+void testSteffense(){
+	cout << "根为：" << Steffensen(1.5, 0.00000001, 10) << endl;
+}
+void testHorner(){
+	cout << "根为:" <<Horner(-2).second << endl;
+	cout << "Muller根为:" << Muller(0.5, 1.0, 1.5, 0.00001, 10, testMuller) << endl;
+}
+
 int main(){
 	testFixedIterator();
 	testNewTonIterator();
-
+	testSteffense();
+	testHorner();
 }