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Diffstat (limited to 'Numerical_Methods_by_E_Balaguruswamy/CH8')
3 files changed, 54 insertions, 0 deletions
diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.1/Ex8_1.R b/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.1/Ex8_1.R new file mode 100644 index 00000000..86ec80bc --- /dev/null +++ b/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.1/Ex8_1.R @@ -0,0 +1,19 @@ +# Example 1 Chapter 8 Page no.: 254
+# Jacobi Iteration Method
+
+# Installing and importing 'pracma' library
+install.packages("pracma")
+library("pracma")
+
+#System of equations in matrix form
+A1 <- matrix(c(2,1,1,3,5,2,2,1,4), nrow = 3, byrow = T)
+B1 <- c(5,15,8)
+
+#Jacobi method
+C <- c()
+C <- itersolve(A1, B1, x0 = NULL, nmax = 4, tol = 1e-05 , method = "Jacobi")
+cat("The values given in the text is only upto 4 iterations, which are:", C[["x"]])
+
+C1 <- c()
+C1 <-itersolve(A1, B1, x0 = NULL, nmax = 1000, tol = 1e-05 , method = "Jacobi")
+cat("The final solution after",C1[["iter"]],"iterations are:", C1[["x"]])
\ No newline at end of file diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.2/Ex8_2.R b/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.2/Ex8_2.R new file mode 100644 index 00000000..759154a8 --- /dev/null +++ b/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.2/Ex8_2.R @@ -0,0 +1,19 @@ +# Example 2 Chapter 8 Page no.: 261
+# Gauss-Seidel Iteration
+
+# Installing and importing 'pracma' library
+install.packages("pracma")
+library("pracma")
+
+#System of equations in matrix form
+A1 <- matrix(c(2,1,1,3,5,2,2,1,4), nrow = 3, byrow = T)
+B1 <- c(5,15,8)
+
+#Gauss-Siedel method
+C <- c()
+C <- itersolve(A1, B1, x0 = NULL, nmax = 2, tol = 1e-05 , method = "Gauss-Seidel")
+cat("The values given in the text is only upto 2 iterations, which are:", C[["x"]])
+
+C1 <- c()
+C1 <-itersolve(A1, B1, x0 = NULL, nmax = 1000, tol = 1e-07 , method = "Gauss-Seidel")
+cat("The final solution after",C1[["iter"]],"iterations are:", C1[["x"]])
\ No newline at end of file diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.3/Ex8_3.R b/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.3/Ex8_3.R new file mode 100644 index 00000000..ffaee94d --- /dev/null +++ b/Numerical_Methods_by_E_Balaguruswamy/CH8/EX8.3/Ex8_3.R @@ -0,0 +1,16 @@ +# Example 3 Chapter 8 Page no.: 269
+# Gauss-Seidel method
+
+# Installing and importing 'pracma' library
+install.packages("pracma")
+library("pracma")
+
+#System of equations in matrix form
+A1 <- matrix(c(3,1,1,-3), nrow = 2, byrow = T)
+B1 <- c(5,5)
+x1 <- c(0,0)
+#Gauss-Siedel method
+C1 <- c()
+C1 <-itersolve(A1, B1, x0 = x1, nmax = 1000, tol = 1e-04 , method = "Gauss-Seidel")
+cat("The final solution after",C1[["iter"]],"iterations are:", C1[["x"]])
+cat("Which can be approximated to x1= 2 and x2= -1")
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