Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
SIAM Journal on Applied Mathematics
Reconstruction of a piecewise constant function from noisy Fourier coefficients by Padé method
SIAM Journal on Applied Mathematics
A new estimation method in modal analysis
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Formulation and solution of structured total least norm problemsfor parameter estimation
IEEE Transactions on Signal Processing
On the distribution of poles of Padé approximants to the Z-transform of complex Gaussian white noise
Journal of Approximation Theory
On the distribution of poles of Padé approximants to the Z-transform of complex Gaussian white noise
Journal of Approximation Theory
Journal of Multivariate Analysis
SIAM Journal on Scientific Computing
Hi-index | 7.29 |
A method for the numerical inversion of the Laplace transform of a continuous positive function f(t) is proposed. Random matrices distributed according to a Gibbs law whose energy V(x) is a function of f(t) are considered as well as random polynomials orthogonal with respect to w(x)=e-V(x). The equation relating w(x) to the reproducing kernel and to the condensed density of the roots of the random orthogonal polynomials is exploited. Basic results from the theories of orthogonal polynomials, random matrices and random polynomials are revisited in order to provide a unified and almost self-contained context. The qualitative behavior of the solutions provided by the proposed method is illustrated by numerical examples and discussed by using logarithmic potentials with external fields that give insight into the asymptotic behavior of the condensed density when the number of data points goes to infinity.