Nicola Mastronardi - Academia.edu (original) (raw)

Papers by Nicola Mastronardi

Siam Journal on Matrix Analysis and Applications, May 1, 2000

In this paper we develop a fast algorithm for the basic deconvolution problem. First we show that... more In this paper we develop a fast algorithm for the basic deconvolution problem. First we show that the kernel problem to be solved in the basic deconvolution problem is a so-called structured Total Least Squares problem. Due to the low displacement rank of the involved matrices, we are able to develop a fast algorithm. We apply the new algorithm on a deconvolution problem arising in a medical application in renography. By means of this example, we show the increased computational performance of our algorithm as compared to other algorithms for solving this type of structured Total Least Squares problems. In addition, Monte-Carlo simulations indicate the superior statistical performance of the structured Total Least Squares estimator compared to other estimators such as the ordinary Total Least Squares estimator.

Eurasip Journal on Advances in Signal Processing, 2007

The cross-fertilization between numerical linear algebra and digital signal processing has been v... more The cross-fertilization between numerical linear algebra and digital signal processing has been very fruitful in the last decades. In particular, signal processing has been making increasingly sophisticated use of linear algebra on both theoretical and algorithmic fronts. The interaction between them has been growing, leading to many new algorithms. In particular, numerical linear algebra tools, such as eigenvalue and singular value decomposition and their higher-extensions, least squares, total least squares, recursive least squares, regularization, orthogonality and projections, are the kernels of powerful and numerically robust algorithms in many signal processing applications.

Siam Journal on Matrix Analysis and Applications, 2010

Many important kernel methods in the machine learning area, such as kernel principal component an... more Many important kernel methods in the machine learning area, such as kernel principal component analysis, feature approximation, denoising, compression, and prediction require the computation of the dominant set of eigenvectors of the symmetric kernel Gram matrix. Recently, an efficient incremental approach was presented for the fast calculation of the dominant kernel eigenbasis. In this paper we propose faster algorithms for incrementally updating and downsizing the dominant kernel eigenbasis. These methods are well-suited for large scale problems since they are efficient in terms of both complexity and data management.

Calcolo

The authors propose and analyze a new algorithm to bound the condition number in spectral norm of... more The authors propose and analyze a new algorithm to bound the condition number in spectral norm of a tridiagonal matrix with nonzero leading principal minors. Examples are given to illustrate the efficiency of the suggested algorithm.

We consider the structured total least squares (STLS) problem. The latter is a natural extension ... more We consider the structured total least squares (STLS) problem. The latter is a natural extension of the ordinary total least squares (TLS) problem and is also used to determine the parameter vector of a linear model given some noisy measurements. We consider structure on two different levels. First of all, the STLS problem is a structured problem, meaning that it extends the TLS formulation by including matrix structure constraints. The structure at this first level is often introduced to obtain statistically more accurate solutions of the parameter vector. Secondly, the matrices involved in algorithms for solving the STLS problem partly inherit the structure imposed by the previously mentioned constraints. Therefore, the structure at this level can be exploited to develop computationally more efficient algorithms. We focus on two particular types of STLS problems using different matrix structure constraints. For both of them fast algorithms are developed by exploiting the low displ...

Standard algorithms for the symmetric tridiagonal eigenvalue problem are mainly based on the QR-i... more Standard algorithms for the symmetric tridiagonal eigenvalue problem are mainly based on the QR-iteration. Another approach presented in the paper, suitable for solving this problem on parallel computers, uses Cuppen’s divide and conquer technique. The proposed scheme deals with the eigensystems of a symmetric arrowhead matrix. The algorithm is demonstrated for the example of the Toeplitz tridiagonal matrices and implemented in MATLAB.Reviewer: Miodrag Petković (Niš)

We present a fast implementation of a recently proposed speech compression scheme, based on an al... more We present a fast implementation of a recently proposed speech compression scheme, based on an all-pole model of the vocal tract. Each frame of the speech signal is analyzed by storing the parameters of the complex damped exponentials deduced from the all-pole model and its initial conditions. In mathematical terms, the analysis stage corresponds to solving a structured total least squares (STLS) problem. It is shown that by exploiting the displacement rank structure of the involved matrices the STLS problem can be solved in a very fast way. Synthesis is computationally very cheap since it consists of adding the complex damped exponentials based on the transmitted parameters.

Rendiconti del Circolo Matematico di Palermo

We consider product integration rules based on generalized Laguerre polynomials, for integrals of... more We consider product integration rules based on generalized Laguerre polynomials, for integrals of type I(f;t)=∫ 0 ∞ f(x)ψ(x,t)dx,t>0,f∈C LOC 0 [ 0 , ∞ ) where ψ(x,t) is a logarithmic or weakly singular algebraic kernel. In particular, we consider the cases of functions ψ(x,t) not necessarily positive and that of oscillating functions ψ(x,t)≡ψ(x). We derive recurrence relations to construct the coefficients of the quadrature rules. Moreover, we prove the stability of the proposed procedure and we state some weighted error estimates in uniform and L 2 norms. Finally, we propose some numerical examples to confirm the theoretical estimates.

The structured total least squares (TLS) problem has been introduced by (4,5) for solving overdet... more The structured total least squares (TLS) problem has been introduced by (4,5) for solving overdetermined linear systems in which both the coecient matrix A; A 2 Rm£n;m ¿ n; and the right{hand side b 2 Rm; are structured and corrupted by noise. The problem can be formulated as the following constrained optimization problem min A; b;x k( A j b)kF such that (A + A)x = b + b and ( A j b) has the same structure as (A j b); This natural extension of the TLS problem is a lot more dicult to solve than the TLS problem, because of its highly nonlinear nature and the existence of many local minima. We focus here on the frequently occurring cases where either (A j b) is a Toeplitz matrix or A a Toeplitz matrix and b unstructured. The structured TLS problem is solved in an iterative fashion, in which, at each iteration, a Least Squares problem involving a rectangular Toeplitz-block matrix needs to be solved. The latter kernel problem is solved in O(mn) ops, via a fast and stable QR decomposition...

We consider a class of integral equations of Volterra type with con- stant coefficients containin... more We consider a class of integral equations of Volterra type with con- stant coefficients containing a logarithmic difference kernel. This class coincides for a = 0 with the Symm's equation. We can transform the general integral equation into an equivalent singular equation of Cauchy type which allows us to give the explicit formula for the solution. The numerical method proposed

Contemporary Mathematics, 2001

KULeuven. ...

Recent progress in signal processing and estimation has gener- ated considerable interest in the ... more Recent progress in signal processing and estimation has gener- ated considerable interest in the problem of computing the smallest eigenvalue of symmetric positive definite Toeplitz matrices. Several algorithms have been proposed in the literature. Many of them com- pute the smallest eigenvalue in an iterative fashion, relying on the Levinson-Durbin solution of sequences of Yule-Walker systems. Exploiting the properties of

Advanced Signal Processing Algorithms, Architectures, and Implementations XII, 2002

The space of all proper rational functions with prescribed real poles is considered. Given a set ... more The space of all proper rational functions with prescribed real poles is considered. Given a set of points zi on the real line and the weights wi, we define the discrete inner product (formula in paper). In this paper we derive an efficient method to compute the coefficients of a recurrence relation generating a set of orthonormal rational basis functions

SIAM Journal on Scientific Computing, 1999

SIAM Journal on Matrix Analysis and Applications, 2008

This issue of SIAM Journal on Matrix Analysis and Applications was motivated by the Workshop on T... more This issue of SIAM Journal on Matrix Analysis and Applications was motivated by the Workshop on Tensor Decompositions and Applications, held in Luminy, France from August 29 to September 2, 2005. The issue was announced through both the SIMAX and the workshop web sites. ...

SIAM Journal on Matrix Analysis and Applications, 2010

The Benzi-Golub result on decay properties for matrix functions of a banded Hermitian matrix is e... more The Benzi-Golub result on decay properties for matrix functions of a banded Hermitian matrix is extended to the case of multi-band and certain other sparse multilevel matrices.