Related papers: A sorting algorithm for complex eigenvalues
This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates…
In this paper we are concerned to find the eigenvalues and eigenvectors of a real symetric matrix by applying a new numerical method similar to Jacobi method. Our approch consists to use a new orthogonal matrix. The computation of the…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
Each year, numerous segmentation and classification algorithms are invented or reused to solve problems where machine vision is needed. Generally, the efficiency of these algorithms is compared against the results given by one or many human…
This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computing eigenvalues located inside a given disk, and the proposed…
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works…
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
Autonomous sorting is a crucial task in industrial robotics which can be very challenging depending on the expected amount of automation. Usually, to decide where to sort an object, the system needs to solve either an instance retrieval…
A new solution strategy for quadratic eigenvalue problems, and the derivatives of the eigenvalues, is proposed, by combining the generalized reduction method with dual numbers. To demonstrate the method, we use the quadratic eigenvalue…
The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…
We present alphaPDE, a new multivariate analysis technique for parameter estimation. The method is based on a direct construction of joint probability densities of known variables and the parameters to be estimated. We show how posterior…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…