answer:Вот пример реализации умножения матриц в Java с помощью Scanner для ввода пользователем матриц: import java.util.Scanner; public class MatrixMultiplication { public static void main(String[] args) { Scanner input = new Scanner(System.in); System.out.print("Введите количество строк первой матрицы: "); int row1 = input.nextInt(); System.out.print("Введите количество столбцов первой матрицы: "); int col1 = input.nextInt(); int[][] matrix1 = new int[row1][col1]; for (int i = 0; i < row1; i++) { for (int j = 0; j < col1; j++) { System.out.print("Введите элемент [" + (i+1) + "][" + (j+1) + "] первой матрицы: "); matrix1[i][j] = input.nextInt(); } } System.out.print("Введите количество строк второй матрицы: "); int row2 = input.nextInt(); System.out.print("Введите количество столбцов второй матрицы: "); int col2 = input.nextInt(); int[][] matrix2 = new int[row2][col2]; for (int i = 0; i < row2; i++) { for (int j = 0; j < col2; j++) { System.out.print("Введите элемент [" + (i+1) + "][" + (j+1) + "] второй матрицы: "); matrix2[i][j] = input.nextInt(); } } if (col1 != row2) { System.out.println("Умножение матриц невозможно!"); } else { int[][] result = new int[row1][col2]; for (int i = 0; i < row1; i++) { for (int j = 0; j < col2; j++) { for (int k = 0; k < col1; k++) { result[i][j] += matrix1[i][k] * matrix2[k][j]; } } } System.out.println("Результат умножения матриц:"); for (int i = 0; i < row1; i++) { for (int j = 0; j < col2; j++) { System.out.print(result[i][j] + "t"); } System.out.println(); } } } }

answer:Конечно, вот пример реализации умножения и заполнения матриц с помощью отдельных методов: import java.util.Scanner; public class MatrixMultiplication { public static void main(String[] args) { Scanner input = new Scanner(System.in); System.out.print("Введите количество строк первой матрицы: "); int row1 = input.nextInt(); System.out.print("Введите количество столбцов первой матрицы: "); int col1 = input.nextInt(); int[][] matrix1 = fillMatrix(row1, col1, input); System.out.print("Введите количество строк второй матрицы: "); int row2 = input.nextInt(); System.out.print("Введите количество столбцов второй матрицы: "); int col2 = input.nextInt(); int[][] matrix2 = fillMatrix(row2, col2, input); if (col1 != row2) { System.out.println("Умножение матриц невозможно!"); } else { int[][] result = multiplyMatrices(matrix1, matrix2); System.out.println("Результат умножения матриц:"); printMatrix(result); } } public static int[][] fillMatrix(int rows, int columns, Scanner input) { int[][] matrix = new int[rows][columns]; for (int i = 0; i < rows; i++) { for (int j = 0; j < columns; j++) { System.out.print("Введите элемент [" + (i+1) + "][" + (j+1) + "] матрицы: "); matrix[i][j] = input.nextInt(); } } return matrix; } public static int[][] multiplyMatrices(int[][] matrix1, int[][] matrix2) { int row1 = matrix1.length; int col1 = matrix1[0].length; int row2 = matrix2.length; int col2 = matrix2[0].length; int[][] result = new int[row1][col2]; for (int i = 0; i < row1; i++) { for (int j = 0; j < col2; j++) { for (int k = 0; k < col1; k++) { result[i][j] += matrix1[i][k] * matrix2[k][j]; } } } return result; } public static void printMatrix(int[][] matrix) { for (int[] row : matrix) { for (int element : row) { System.out.print(element + "t"); } System.out.println(); } } }

answer:Here is a Matlab function that implements the "Pure" QR Algorithm with the given convergence conditions: ```matlab function [D, Q, iter] = ubitname_final_D1(A, tol) % Ensure that A is real and symmetric if ~isreal(A) || ~issymmetric(A) error('A must be a real and symmetric matrix.') end n = size(A, 1); D = A; % Initialize D with A Q = eye(n); % Initialize Q as the identity matrix iter = 0; % Iterate until the convergence condition is met while true iter = iter + 1; % Perform the QR decomposition [Qiter, R] = qr(D); % Update D and Q D = R * Qiter; Q = Q * Qiter; % Calculate the convergence criterion T_diag = diag(D); T_subdiag = diag(D, -1); convergence = norm(T_subdiag, 2) / norm(T_diag, 2); % Check if the method has converged if convergence < tol break; end end end ``` To use the function, simply provide a real and symmetric matrix A and a tolerance value, like this: ```matlab % Define a real symmetric matrix A A = [1 2 3; 2 4 5; 3 5 6]; % Define the tolerance for convergence tol = 1e-6; % Calculate the eigenvalues and eigenvectors using the "Pure" QR Algorithm [D, Q, iter] = ubitname_final_D1(A, tol); % Display the results disp('Eigenvalues (D): '); disp(D); disp('Eigenvectors (Q): '); disp(Q); disp(['Number of iterations: ', num2str(iter)]); ``` This code implements the "Pure" QR Algorithm as described in the problem statement and satisfies the given convergence conditions.

answer:Here is a Matlab function that implements the QR Algorithm with the Wilkinson shift, using the same inputs and outputs as the previous function: ```matlab function [D, Q, iter] = ubitname_final_p2(A, tol) % Ensure that A is real and symmetric if ~isreal(A) || ~issymmetric(A) error('A must be a real and symmetric matrix.') end n = size(A, 1); D = A; % Initialize D with A Q = eye(n); % Initialize Q as the identity matrix iter = 0; % Iterate until the convergence condition is met while true iter = iter + 1; % Calculate the Wilkinson shift delta = (D(end - 1, end - 1) - D(end, end)) / 2; sigma = D(end, end) - sign(delta) * D(end, end - 1)^2 / ... (abs(delta) + sqrt(delta^2 + D(end, end - 1)^2)); % Apply the shift D = D - sigma * eye(n); % Perform the QR decomposition [Qiter, R] = qr(D); % Update D and Q D = R * Qiter + sigma * eye(n); Q = Q * Qiter; % Calculate the convergence criterion T_diag = diag(D); T_subdiag = diag(D, -1); convergence = norm(T_subdiag, 2) / norm(T_diag, 2); % Check if the method has converged if convergence < tol break; end end end ``` To use the function, simply provide a real and symmetric matrix A and a tolerance value, like this: ```matlab % Define a real symmetric matrix A A = [1 2 3; 2 4 5; 3 5 6]; % Define the tolerance for convergence tol = 1e-6; % Calculate the eigenvalues and eigenvectors using the QR Algorithm with Wilkinson shift [D, Q, iter] = ubitname_final_p2(A, tol); % Display the results disp('Eigenvalues (D): '); disp(D); disp('Eigenvectors (Q): '); disp(Q); disp(['Number of iterations: ', num2str(iter)]); ``` This code implements the QR Algorithm with the Wilkinson shift as described and satisfies the given convergence conditions.