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Showing 1 to 14 of 14 for “"Matrix Functions"”.
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Zero-pole interpolation of nonregular rational matrix functions
… structure of a not necessarily regular rational matrix function W is described in terms of pairs of matrices-right and left pole pairs. The concept of orthogonality in R<sup>n</sup> is investigated. Using this concept, the right and left zero structure of a rational matrix function W is described …
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Interpolation by rational matrix functions with minimal McMillan degree
Interpolation conditions on rational matrix functions expressed in terms of residues are studied. As a compact way of expressing tangential interpolation conditions of arbitrarily high multiplicity possibly from both sides simultaneously, interpolation conditions are represented in terms of …
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Graph diffusions and matrix functions: fast algorithms and localization results
… Whereas many standard graph algorithms rely on matrix-vector operations that require exploring the entire graph, this thesis is concerned with graph algorithms that are local (that explore only the graph region near the nodes of interest) as well as the localized behavior of global algorithms. …
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The computation of matrix functions in particular, the matrix exponential
Matrix functions in general are an interesting area in matrix analysis and are used in many areas of linear algebra and arise in numerous applications in science and engineering. We consider how to define matrix functions and how to compute matrix functions. To be concrete, we pay particular …
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Functional quantum algorithms: a mélange of methods for matrix functions
… unitary processes by near arbitrary continuous functions, and this simple ability—computing matrix functions quantum mechanically—has been shown to subsume diverse tasks with comparatively simple complexity analysis. This thesis claims and provides a series of constructions supporting that QSP …
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Rapid Approximation of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis of Gaussian Node Placement
<p>Technological advancements have allowed computing power to generate high resolution model s. As a result, greater stiffness has been introduced into systems of ordinary differential equations (ODEs) that arise from spatial discreti zation of partial differential equations (PDEs). The components …
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A new block Krylov subspace framework with applications to functions of matrices acting on multiple vectors
… block Krylov subspace methods, which hinges on a matrix-valued inner product. We can recast the ``classical" block Krylov methods, such as O'Leary's block conjugate gradients, global methods, and loop-interchange methods, within this framework. Leveraging the generality of the framework, we …
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Quantum Algorithms for Matrix Problems and Machine Learning
… algorithms for problems that can be posed as matrix function tasks. In Chapter 1 we demonstrate a simple unifying framework for implementing of smooth functions of matrices on a quantum computer. This framework captures a variety of problems that can be solved by evaluating properties of some …
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Singular integral equations and realization: A survey of the state space method
… This method is based on the fact that a rational matrix function VV(^) which is analytic and invertible at infinity can be represented by vv(^): D * C(AI - A)-'B, (0.1) where A is a square matrix whose order may be larger than that of I,7()), and .8. C and D are matrices of appropriate sizes. The …
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The structure and function of TasA in the <i>Bacillus subtilis</i> biofilm matrix
… encompassed within a self-produced extracellular matrix. The matrix functions to shield the interior cells from biotic and abiotic stresses and to retain nutrients and signalling molecules. The multiple functions of the biofilm matrix are mediated by the constituent parts which may include a …
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Polynomial-Based Methods for Time-Integration
… simple procedure for initializing the requisite matrix functions. We compare the stability and accuracy properties of our new exponential methods to those of an existing implicit-explicit spectral deferred correction scheme. We find that exponential integrators have larger accuracy regions and …
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Several Problems Concerning Multivariate Functions and Associated Operators
… two distinct problems about multivariate functions and their associated operators. It first discusses the structure of Agler decompositions, which give useful ways to represent two-variable Schur functions on the bidisk using positive kernels. An elementary proof of the existence of Agler …
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Numerical Methods in Deep Learning and Computer Vision
… techniques mainly include differentiable matrix power functions, differentiable eigendecomposition (ED), feasible orthogonal matrix constraints in optimization and latent semantics discovery, and physics-informed techniques for solving partial differential equations in disentangled and …
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Elucidating the Response of Activated Sludge Cultures to Toxic Chemicals at the Process, Floc and Metabolic Scales
… study, we were able to establish a source-effect matrix linking classes of chemical toxins to their potential inhibitory effects on activated sludge processes, thereby contributing to a better understanding of the potential effects of toxic industrial discharges into biological treatment systems. …