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Error analysis for a class of degenerate-kernel methods
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In this article, convergence theorems for a class of degenerate-kernel methods for numerical solution of Fredholm integral equations of the second kind were proved. And it was shown that the simplest of these methods has a faster rate of convergence than the simple method of moments, or Galerkin method, even though its computational requirements are almost identical.Abstract:
Convergence theorems are proved for a recently proposed class of degenerate-kernel methods for the numerical solution of Fredholm integral equations of the second kind. In particular, it is shown that the simplest of these methods has a faster rate of convergence than the simple method of moments, or Galerkin method, even though its computational requirements are almost identical.read more
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Projection Methods
TL;DR: Virtually all iterative methods for solving Ax = b can be cast as projection methods, from simple Gauss-Seidel, to Conjugate Gradients, to multigrid methods, and this work introduces them here for several reasons.
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Improvement by iteration for compact operator equations
TL;DR: In this paper, it was shown that if Yln is chosen optimally (i.e. if the coefficients ani are chosen to minimize Ily Yln 11), and if Y2n is chosen to be the first iterate of Ylnl i.i.d.
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The Spectral Approximation of Linear Operators with Applications to the Computation of Eigenelements of Differential and Integral Operators
TL;DR: In this article, the numerical solution of the eigenvalue problem is studied, where T is a linear operator in a Bana,ch space and T may represent a bounded integral operator or a closed differential operator with bounded inverse.
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Acceleration by aggregation of successive approximation methods
TL;DR: Methods of successive approximation for solving linear systems or minimization problems are accelerated by aggregation-disaggregation processes, characterized by means of Galerkin approximations, and this in turn permits analysis of the method.
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Galerkin methods for second kind integral equations with singularities
TL;DR: In this article, the numerical solution of the second kind of integral equations with weakly singular kernels and inhomogeneous terms is discussed and global convergence estimates are derived for the Galerkin and iterated GAs using splines on arbitrary quasi-uniform meshes as approximating subspaces.
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Related Papers (5)
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