Finding the matrix hyperbolic sine function using Taylor series.

Here’s an example of a Java program that calculates the matrix hyperbolic sine function using the Taylor series approximation:

 import java.util.Arrays;

 public class MatrixHyperbolicSine {

    // Function to calculate the matrix hyperbolic sine

    public static double[][] calculateHyperbolicSine(double[][] matrix, int iterations) {

        int rows = matrix.length;

        int cols = matrix[0].length;

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

        // Iterate over each element in the matrix

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

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

                double currentElement = matrix[i][j];

                double sum = 0.0;

                // Compute the Taylor series approximation

                for (int k = 0; k < iterations; k++) {

                    int sign = (k % 2 == 0) ? 1 : -1;

                    double power = 2 * k + 1;

                    double term = Math.pow(currentElement, power) / factorial(power);

                    sum += sign * term;

                }

                result[i][j] = sum;

            }

        }

        return result;

    }
    // Function to calculate the factorial of a number

    public static double factorial(double n) {

        if (n == 0 || n == 1)

            return 1;

        double result = 1;

        for (double i = 2; i <= n; i++)

            result *= i;

        return result;

    }
    public static void main(String[] args) {

        double[][] matrix = {

            {1.0, 2.0, 3.0},

            {4.0, 5.0, 6.0},

            {7.0, 8.0, 9.0}

        };

        int iterations = 10;

        double[][] result = calculateHyperbolicSine(matrix, iterations);

        // Print the resulting matrix

        for (double[] row : result) {

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

        }

    }

}

In this example, the `calculateHyperbolicSine` method takes a matrix and the number of iterations as input. It then applies the Taylor series approximation for the hyperbolic sine function to each element in the matrix. The `factorial` method calculates the factorial of a given number.

In the `main` method, we define a sample matrix and the number of iterations to perform. We then call the `calculateHyperbolicSine` method to obtain the result, which is printed to the console.