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Explicit Error Estimation for Boundary Value Problems, partial differential equations. These error estimates are crucial for obtaining explicit eigenvalue bounds. A primary focus is on the a priori error estimation based on the hypercircle method (i.e., the Prager–Synge theorem), offering a novel approach for projection error estimation in the analysis of eigenvalue problems.

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Explicit Eigenvalue Bounds for Various Differential Operators,raditional model eigenvalue problems involving the Laplace, the biharmonic, the Stokes, and the Steklov differential operators. For each problem, the Galerkin projection error constant . is evaluated explicitly to obtain lower eigenvalue bounds.

AMITY

Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems978-981-97-3577-8Series ISSN 2191-8198 Series E-ISSN 2191-8201

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intolerance

Introduction to Eigenvalue Problems,ogress in the field of guaranteed eigenvalue computation over the past decade, while also highlighting its relationship with early work such as Birkhoff’s result. Examples of eigenvalue problems demonstrate the need for guaranteed computation. The chapter also discusses the settings of function spac

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Explicit Error Estimation for Boundary Value Problems, partial differential equations. These error estimates are crucial for obtaining explicit eigenvalue bounds. A primary focus is on the a priori error estimation based on the hypercircle method (i.e., the Prager–Synge theorem), offering a novel approach for projection error estimation in the analysis

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Explicit Eigenvalue Bounds for Various Differential Operators,raditional model eigenvalue problems involving the Laplace, the biharmonic, the Stokes, and the Steklov differential operators. For each problem, the Galerkin projection error constant . is evaluated explicitly to obtain lower eigenvalue bounds.

Grasping

,Lehmann–Goerisch Method for High-Precision Eigenvalue Bounds,s a feature of this book, it discloses the affinity of the Lehmann–Goerisch method with finite element methods, which has not been well discussed in the existing literature. The implementation of the Lehmann–Goerisch method necessitates a rough lower bound for a specific eigenvalue, which can be obt

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Guaranteed Eigenfunction Computation,tinct algorithms depending on problem settings: the Rayleigh quotient-based algorithm, the residual-based algorithm, and the projection-based algorithm. Particular emphasis is placed on the residual-based error estimation, including an in-depth discussion on the Davis-Kahan theorem extended to weakl