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A direct data-driven iterative algorithm is developed to accurately estimate the $H_\infty$ norm of a linear time-invariant system from continuous operation, i.e., without resetting the system. The main technical step involves a…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…
We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we…
Parametrization of complex 4 x 4 - matrices G in terms of Dirac tensor parameters (A,B,A_{l},B_{l},F_{kl}) or equivalent four complex 4-vectors (k,m,n,l) is investigated. In the given parametrization, the problem of inverting any 4 x 4…
Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the…
Principal component analysis (PCA) is a powerful tool for dimensionality reduction. Unfortunately, it is sensitive to outliers, so that various robust PCA variants were proposed in the literature. Among them the so-called rotational…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm…
A formula for the Riemannian metric tensor of differentiable manifolds of linear dynamical systems of same McMillan degree is presented in terms of their transfer function matrices. The necessary calculations for its application to ARMA and…
In this paper, we develop rapidly convergent forward-backward algorithms for computing zeroes of the sum of finitely many maximally monotone operators. A modification of the classical forward-backward method for two general operators is…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…
High-throughput neural network inference requires coordinating many optimization decisions, including parallel tiling, microkernel selection, and data layout. The product of these decisions forms a search space of programs which is…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
By the Fourier transformations, any group-invariant functions over finite Abelian groups are transformed into group-invariant functions over the character groups. In this paper, we calculate matrix elements of this transformations under…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
A recently developed numerical method for the calculation of derivatives of functions of general complex matrices, which can also be combined with implicit matrix function approximations such as Krylov-Ritz type algorithms, is presented. An…
The resultant of two univariate polynomials is an invariant of great importance in commutative algebra and vastly used in computer algebra systems. Here we present an algorithm to compute it over Artinian principal rings with a modified…
We fix three natural numbers $k, n, N$, such that $n+k+1=N$, and introduce the notion of two dual arrangements of hyperplanes. One of the arrangements is an arrangement of $N$ hyperplanes in a $k$-dimensional affine space, the other is an…