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- Tharmalingam Ratnarajah, Rémi Vaillancourt, M. Alvo
- SIAM J. Matrix Analysis Applications
- 2004

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)

- Tharmalingam Ratnarajah, Rémi Vaillancourt, M. Alvo
- Probl. Inf. Transm.
- 2005

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)

- Tharmalingam Ratnarajah, Rémi Vaillancourt
- IEEE Transactions on Information Theory
- 2005

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)

In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m × m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n… (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)

- Tharmalingam Ratnarajah, Rémi Vaillancourt
- 2004 IEEE International Conference on Acoustics…
- 2004

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)

- Mawardi Bahri, Ryuichi Ashino, Rémi Vaillancourt
- Applied Mathematics and Computation
- 2011

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)