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A fast quantum algorithm for solving partial differential equations. [PDF]
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The Classical Iterative Methods
2020Show that if aii = d ≠ 0 for all i then Richardson’s method with α:= 1=d is the same as Jacobi’s method.
Georg Muntingh, Øyvind Ryan, Tom Lyche
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Iterating the nonclassical symmeteries method
Physica D: Nonlinear Phenomena, 1994We show that iterations of the nonclassical symmetries method for any evolution equation give raise to new nonlinear equations, which inherit the symmetry algebra of the given equation. Invariant solutions of these heir-equations supply new solutions of the original equation.
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1993
Publisher Summary This chapter discusses a few iterative methods based on relaxation. The iterative methods have more modest storage requirements than direct methods and are also faster, depending on the iterative method and the problem. They usually also have better vectorization and parallelization properties. The Jacobi method is sometimes known as
Gene Golub, James M. Ortega
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Publisher Summary This chapter discusses a few iterative methods based on relaxation. The iterative methods have more modest storage requirements than direct methods and are also faster, depending on the iterative method and the problem. They usually also have better vectorization and parallelization properties. The Jacobi method is sometimes known as
Gene Golub, James M. Ortega
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1994
This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for ...
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This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for ...
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, 1993 In Part I of this lecture, the iterative COC algorithm is described in detail and then it is illustrated with beam and plate (plane stress) examples for a variety of design constraints. For trusses with stress constraints and a deflection constraint an independent derivation of the optimality criteria is presented and then the method is illustrated by ...
Ming Zhou, George I. N. Rozvany
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Padé iteration method for regularization
Applied Mathematics and Computation, 2006Abstract In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k, j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov.
Kirsche, Andreas, Böckmann, Christine
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1994
The semi-iteration comes in three formulations. The first one in Section 8.1 is the most general and associates each semi-iterate with a polynomial. Using the notion of Krylov spaces, we only require that the errors of the semi-iterates \(y^{m}\) be elements of the Krylov space \(x^{0}+N\mathcal {K}_{m}(AN,r^{0})\). In the second formulation of Section
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The semi-iteration comes in three formulations. The first one in Section 8.1 is the most general and associates each semi-iterate with a polynomial. Using the notion of Krylov spaces, we only require that the errors of the semi-iterates \(y^{m}\) be elements of the Krylov space \(x^{0}+N\mathcal {K}_{m}(AN,r^{0})\). In the second formulation of Section
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The Mathematics Teacher, 1964
Iteration for its own sake but also as a device for relating important mathematical ...
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Iteration for its own sake but also as a device for relating important mathematical ...
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1966
Publisher Summary This chapter discusses the fixed-point theorem for a general iterative method in pseudometric spaces. It discusses the conditions under which the iterations can be carried out without further restrictions, that is, the sequence un converges, and the limit element u satisfies the operator equation Tu =u.
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Publisher Summary This chapter discusses the fixed-point theorem for a general iterative method in pseudometric spaces. It discusses the conditions under which the iterations can be carried out without further restrictions, that is, the sequence un converges, and the limit element u satisfies the operator equation Tu =u.
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