
Numerical methods for differential linear matrix equations via Krylov subspace methods
In the present paper, we present some numerical methods for computing ap...
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Effective Matrix Methods in Commutative Domains
Effective matrix methods for solving standard linear algebra problems in...
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Frequency extraction for BEMmatrices arising from the 3D scalar Helmholtz equation
The discretisation of boundary integral equations for the scalar Helmhol...
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Explicit Solutions of the Singular Yang–Baxterlike Matrix Equation and Their Numerical Computation
We derive several explicit formulae for finding infinitely many solution...
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Optimal Finegrained Hardness of Approximation of Linear Equations
The problem of solving linear systems is one of the most fundamental pro...
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Rational Krylov and ADI iteration for infinite size quasiToeplitz matrix equations
We consider a class of linear matrix equations involving semiinfinite m...
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KrylovSimplex method that minimizes the residual in ℓ_1norm or ℓ_∞norm
The paper presents two variants of a KrylovSimplex iterative method tha...
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Iterative optimal solutions of linear matrix equations for Hyperspectral and Multispectral image fusing
For a linear matrix function f in X ∈^m× n we consider inhomogeneous linear matrix equations f(X) = E for E ≠ 0 that have or do not have solutions. For such systems we compute optimal norm constrained solutions iteratively using the Conjugate Gradient and Lanczos' methods in combination with the MoreSorensen optimizer. We build codes for ten linear matrix equations, of Sylvester, Lyapunov, Stein and structured types and their Tversions, that differ only in two five times repeated equation specific code lines. Numerical experiments with linear matrix equations are performed that illustrate universality and efficiency of our method for dense and small data matrices, as well as for sparse and certain structured input matrices. Specifically we show how to adapt our universal method for sparse inputs and for structured data such as encountered when fusing image data sets via a Sylvester equation algorithm to obtain an image of higher resolution.
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