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In this paper, the distributions of the largest and smallest eigenvalues of complex Wishart matrices and the condition number of complex Gaussian random matrices are derived. These distributions are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. Several results are derived(More)
The eigenvalue densities of complex noncentral Wishart matrices are investigated to study an open problem in information theory. Specifically, the largest, smallest and joint eigenvalue densities of complex noncentral Wishart matrices are derived. These densities are expressed in terms of complex zonal polynomials and invariant polynomials. The connection(More)
In this correspondence, the densities of quadratic forms on complex random matrices and their joint eigenvalue densities are derived for applications to information theory. These densities are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. The derived densities are used to(More)
A 3-stage 6-step variable step Hermite-Birk-hoff-Obrechkoff method of order 14, denoted by HBO14(3,6), is constructed for solving non-stiff systems of first-order differential equations of the form y = f (x, y), y(x 0) = y 0. Its formula uses y and y as in Obrechkoff method. Forcing a Taylor expansion of the numerical solution to agree with an expansion of(More)
Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff methods of order 4 to 14, denoted by HBO(4-14)3, are constructed for solving non-stiff systems of first-order differential equations of the form y = f (x, y), y(x 0) = y 0. These methods use y and y as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an(More)
The paper explains the concepts of order and absolute stability of numerical methods for solving systems of first-order ordinary differential equations (ODE) of the form y = f (t, y), y(t 0) = y 0 , where f : R × R n → R n , describes the phenomenon of problem stiffness, and reviews explicit Runge–Kutta methods, and explicit and implicit linear multistep(More)
Quadratic forms on complex random matrices and their joint eigenvalue densities are derived with the goal of studying the ergodic channel capacity of multiple-input multiple-output (MIMO) Rayleigh distributed wireless communication channels. We consider MIMO channels which are correlated at the transmitter and/or the receiver ends and evaluate the(More)
In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular(More)