Finding the matrix hyperbolic cosine function using Taylor series.

Here’s a Java program that calculates the matrix hyperbolic cosine function using the Taylor series approximation:

  import java.util.Arrays;

   public class MatrixHyperbolicCosine {

    public static void main(String[] args) {

        double[][] matrix = {{1, 2}, {3, 4}}; // Example matrix

        double[][] matrixCosh = matrixCosh(matrix);

        System.out.println("Matrix Hyperbolic Cosine:");

        printMatrix(matrixCosh);

    }

    public static double[][] matrixCosh(double[][] matrix) {

        int rows = matrix.length;

        int cols = matrix[0].length;

        double[][] result = new double[rows][cols];

        for (int i = 0; i < rows; i++) {

            for (int j = 0; j < cols; j++) {

                result[i][j] = calculateCosh(matrix[i][j]);

            }

        }    

        return result;

    }

    public static double calculateCosh(double x) {

        int iterations = 10; // Number of terms to approximate

        double result = 1;

        double term = 1;

        for (int i = 1; i <= iterations; i++) {

            term *= x * x / (2 * i * (2 * i - 1));

            result += term;

        }

        return result;

    }

    public static void printMatrix(double[][] matrix) {

        for (double[] row : matrix) {

            System.out.println(Arrays.toString(row));

        }

    }

}

This program defines a `matrixCosh` function that takes a matrix as input and returns the matrix hyperbolic cosine of each element. The `calculateCosh` function approximates the hyperbolic cosine using the Taylor series with a specified number of iterations.

In the example above, the program calculates the matrix hyperbolic cosine for a 2×2 matrix and prints the resulting matrix. You can modify the `matrix` variable to use a different matrix if needed.