?0 ?0
?0 C?0
?n ?n
A01=Anatoly Galperin
Affine Function
Age Group_Uncategorized
Age Group_Uncategorized
Approximation Ln
Author_Anatoly Galperin
automatic-update
Banach Space
Banach Spaces
Banach spaces analysis
BFGS Update
Broyden's method
Broyden's Update
Broyden’s Method
Broyden’s Update
Category1=Non-Fiction
Category=PBK
Convergence Domain
convergence theory
COP=United States
Delivery_Delivery within 10-20 working days
Differentiable Operators
Divided Difference Operator
eq_isMigrated=2
eq_nobargain
functional analysis advanced
Functional Equation
General Iterative Method
Hilbert Space
Hilbert space methods
Interior Maximum
Iterative Methods
iterative solution regular continuity
Language_English
Linear Bounded Operator
Lipschitz Continuity
Minimal Frobenius Norm
Minimum Condition Number
Modified Newton Method
Nonlinear Functional Analysis
nonlinear operator equations
PA=Available
Price_€100 and above
PS=Active
Secant Update
secant-type algorithms
Sequence Xn
softlaunch
Starters X0
Ulm's method
Γ0 Cβ0
Γ0 Β0
Γn Βn
Product details
- ISBN 9781498758925
- Weight: 476g
- Dimensions: 156 x 234mm
- Publication Date: 26 Oct 2016
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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Iterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm’s and Broyden’s methods. Convergence analyses of the methods considered are based on Kantorovich’s majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity.
Key Features
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- The methods discussed are analyzed under the assumption of regular continuity of divided difference operator, which is more general and more flexible than the traditional Lipschitz continuity.
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- An attention is given to criterions for comparison of merits of various methods and to the related concept of optimality of a method of certain class.
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- Many publications on methods for solving nonlinear operator equations discuss methods that involve inversion of linearization of the operator, which task is highly problematic in infinite dimensions.
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- Accessible for anyone with minimal exposure to nonlinear functional analysis.
