The Numerical Methods For The Correlation Matrix And Complex Conjugate Linear Matrix Equations

Correlation matrix plays a very important role in a great many areas of finance and risk management, for instance, credit-derivative pricing, stress-testing and scenario analysis for market risk management purpose. Thus, it is of great value to study how to find the nearest correlation matrix close to the given matrix. It is one of the main contents discussed in the paper. In addition, we study a group of complex conjugate linear matrix equations and give a real finite iterative algorithm to compute the common solution of the equations.The nearest correlation matrix have been discussed in many papers, theories and numerical methods have been proposed. A modified alternative gradients algorithm is presented to compute the nearest correlation matrix with the aid of Armijo rule, the convergence property is analyzed in detail. Numerical experiments show that the proposed algorithm is efficient.For a group of complex matrix equations, a new iterative method based on the real representation of a complex matrix is proposed. The complex operations are avoided in this method. Furthermore, the method can be extended to solve a more general group of complex matrix equations.