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Showing 1 to 8 of 8 for “"Numerical range."”.
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On the Numerical Range of Compact Operators
… (theorem 25). It is<br />well known that the numerical range of a bounded operator on a finite dimensional<br />Hilbert space is closed (theorem 54). In this thesis we explore how close to being<br />closed the numerical range of a compact operator is (theorem 56). We also describe<br />how …
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Exploring the Numerical Range of Block Toeplitz Operators
<p>We will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary …
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Higher Rank Numerical Ranges for Certain Non-Normal Matrices
This thesis undertakes the study of higher rank numerical ranges for certain non-normal matrices, namely direct sums of Jordan blocks, and direct sums of the form (Jordan Block plus scalar multiple of the identity). The higher rank numerical range of a normal matrix is well-understood, but little …
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Convergence of the Arnoldi Iteration for Estimating Extreme Eigenvalues
… convergence of Krylov methods for estimating the numerical range of a matrix. Prior bounds on approximation error often depend on eigenvalue gaps of the matrix, which lead to weaker bounds than observed in practice, specifically in applications where these gaps are small. Instead, we extend a line …
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Modeling variability for biologics strategic planning
… model forecasts variability and displays a numerical range of projects and headcount requirements expected for several years. This data is essential for project managers, function heads, and operations leaders to develop the five-year strategic plan for biologic development. This model …
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Mathematical Modeling and Dynamic Recovery of Power Systems
… with classical bounds based on the spectrum, numerical range, and pseudospectra. We show how Godunov's bounds can be optimized to bound the solution operator at a given time. The Loewner framework provides a tool for identifying a dynamical system from tangential measurements. The singular …
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SEISMIC SIGNATURES OF PORE CONNECTIVITY
… the extent of pore connectivity that has the numerical range from 0 to 1. In the second part, with other assumed medium parameters, calculation results show friability has observable seismic signatures. Most of them have very large, non-monotonic, and nonlinear variations to friability. …
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Poncelet polygons through the lenses of orthogonal polynomials on the unit circle, finite Blaschke products, and numerical ranges.
The topics in this thesis fall in the intersection of projective geometry, complex analysis, and linear algebra. Each of these three fields gives a canonical construc-tion of families of polygons inscribed in the unit circle with interlacing vertices. In projective geometry, we consider Poncelet …