Results 111 to 120 of about 5,798 (159)
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1977
As before, let A be a positive definite operator on a linear set D A in a separable Hilbert space H, and let f ∈ H. Let H A be the Hilbert space of Chap. 10 (thus separable because H is separable, see p. 146). In H A consider a base (i.e., an at most countable linearly independent complete system) $$ {{\varphi }_{1}},{{\varphi }_{2}}, \ldots {\text{
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As before, let A be a positive definite operator on a linear set D A in a separable Hilbert space H, and let f ∈ H. Let H A be the Hilbert space of Chap. 10 (thus separable because H is separable, see p. 146). In H A consider a base (i.e., an at most countable linearly independent complete system) $$ {{\varphi }_{1}},{{\varphi }_{2}}, \ldots {\text{
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A ritz method for an optimal control problem
Journal of Optimization Theory and Applications, 1973We generalize and simplify the proofs of the basic papers of Bosarge and Johnson (Refs. 1-3) on a variational procedure for approximating the solution of thestate regular problem. We derive generala priori error bounds for this procedure and apply these results to obtain asymptotic error bounds for the special case of spline-type approximations.
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Vibration of Rectangular Plates by the Ritz Method
Journal of Applied Mechanics, 1950Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection.
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On the Numerical Stability of the Rayleigh–Ritz Method
SIAM Journal on Numerical Analysis, 1977The numerical stability of the Rayleigh–Ritz method is investigated from the point of view of Mikhlin stability and of the condition number of the Rayleigh–Ritz matrix, and it is shown that the condition number approach is more appropriate for floating-point computation.
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2013
This is the first of two chapters devoted to the approximate analysis of continuous systems. In this chapter, a global method of approximation is considered: the Rayleigh-Ritz method. It is based on the definition of a set of global assumed modes defined on the entire domain and satisfying the kinematic boundary conditions.
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This is the first of two chapters devoted to the approximate analysis of continuous systems. In this chapter, a global method of approximation is considered: the Rayleigh-Ritz method. It is based on the definition of a set of global assumed modes defined on the entire domain and satisfying the kinematic boundary conditions.
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Journal of Mathematical Chemistry
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COMBINATIONS OF THE RITZ-GALERKIN AND FINITE DIFFERENCE METHODS
International Journal for Numerical Methods in Engineering, 1996This paper presents six combinations of the Ritz-Galerkin method and the finite difference method for solving elliptic boundary value problems. Not only optimal convergence rates of solutions but also superconvergence rates of solution derivatives can be achieved.
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Method of Ritz for random eigenvalue problems
Kybernetika, 1994Summary: Boundary value problems for ordinary differential equations with random coefficients are dealt with. Asymptotic normality of the eigenvalues is derived under proper conditions. The method of Ritz enables to extend the results. Application of the presented theory in dynamics is added.
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The Ritz Method in the Eigenvalue Problem
1977Consider the eigenvalue problem for the equation $$Au - \lambda u = 0.$$ (40.1) with homogeneous boundary conditions, thus — in the weak formulation — the problem $$u \in V,\,u \ne 0,$$ (40.2) $$\left( {\left( {v,u} \right)} \right) - \lambda \left( {v,u} \right) = 0\,\,\,\,for\,every\,\,\,v \in V.$$ (40.3)
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