Related papers: On the Jacobi formula for Bivariate Pade Approxima…
In paper a new definition of reduced Pade approximant and algorithm for its computing is proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Pade approximant…
Dual quaternion matrices have various applications in robotic research and its spectral theory has been extensively studied in recent years. In this paper, we extend Jacobi method to compute all eigenpairs of dual quaternion Hermitian…
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…
Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining B\'{e}zier form of the $L^2$-solution of the problem of best polynomial approximation of B\'{e}zier curve or surface. In this connection, the…
For a given $\theta\in (-1,1)$, we find out all parameters $\alpha,\beta\in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(\alpha,\beta)}(x)-C J_{n}^{(\alpha,\beta)}(x)$ which generates a Lobatto…
In solving the variational problem, the key is to efficiently find the target function that minimizes or maximizes the specified functional. In this paper, by using the Pade approximant, we suggest a methods for the variational problem. By…
In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012--4024, with respect to the convergence of the accelerated Riccati iteration method for solving the…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
Jacobi-type algorithms for simultaneous approximate diagonalization of real (or complex) symmetric tensors have been widely used in independent component analysis (ICA) because of their good performance. One natural way of choosing the…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
This paper establishes the iteration-complexity of a Jacobi-type non-Euclidean proximal alternating direction method of multipliers (ADMM) for solving multi-block linearly constrained nonconvex programs. The subproblems of this ADMM variant…
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
A systematic numerical approach to approximate high dimensional Lindblad equations is described. It is based on a deterministic rank m approximation of the density operator, the rank m being the only parameter to adjust. From a known…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…