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Fiedler Linearizations of Rectangular Rational Matrix Functions
Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational...
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Realizations of Non-commutative Rational Functions Around a Matrix Centre, II: The Lost-Abbey Conditions
In a previous paper the authors generalized classical results on minimal realizations of non-commutative (nc) rational functions, using nc...
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Factorization of the Partly Non-rational Matrix of Arbitrary Order
AbstractIt is proposed a constructive method of factorization of partly non-rational matrix-functions of an arbitrary order. The algorithm is...
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Taylor Polynomials of Rational Functions
A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and...
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Convergence for noncommutative rational functions evaluated in random matrices
One of the main applications of free probability is to show that for appropriately chosen independent copies of d random matrix models, any...
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When rational functions meet virtual elements: the lightning virtual element method
We propose a lightning Virtual Element Method that eliminates the stabilisation term by actually computing the virtual component of the local VEM...
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On axially rational regular functions and Schur analysis in the Clifford-Appell setting
In this paper we start the study of Schur analysis for Cauchy–Fueter regular quaternionic-valued functions, i.e. null solutions of the Cauchy–Fueter...
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On refined rational convex contractions with applications to matrix and implicit functional integral equations
This research presents an advancement in fixed point theory by extending the renowned Banach contractive condition and introducing the new convex...
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Bounding Zolotarev Numbers Using Faber Rational Functions
By closely following a construction by Ganelius, we use Faber rational functions to derive tight explicit bounds on Zolotarev numbers. We use our...
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Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations
In this work, a numerical technique for solving general nonlinear ordinary differential equations (ODEs) with variable coefficients and given...
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Extended barycentric rational schemes for functions of singularities
In this paper, we propose two kinds of extended barycentric rational schemes via (non-conformally) scaled transformations for approximating functions...
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Algebraic Functions: Polynomial, Rational and Irrational
The preceding sections have prepared a basis for detailed analysis of different specific functions and construction of their graphs. In this chapter...
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Solving Continuous Time Leech Problems for Rational Operator Functions
The main continuous time Leech problems considered in this paper are based on stable rational finite dimensional operator-valued functions G and K ....
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Two-dimensional topological theories, rational functions and their tensor envelopes
We study generalized Deligne categories and related tensor envelopes for the universal two-dimensional cobordism theories described by rational...
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The Rational Interpolation Problem: Grassmannian and Loewner-Matrix Approaches
We review the Grassmannian approach to rational interpolation theory and indicate points of contact and divergence with the Loewner-matrix approach....