Description |
1 online resource (280 pages) |
Series |
Inverse and ill-posed problems series |
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Inverse and ill-posed problems series.
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Contents |
Chapter 1. The basic concepts of inverse and ill-posed problems -- Â1 Inverse problems. The examples -- Â2 Well-posed and ill-posed problems -- Â3 Operator equations of the first and the second kinds -- Â4 Some aspects of setting and solving inverse problems -- Â5 Exercises for readers -- Chapter 2. Inverse problems for ordinary differential equations -- Â1 Problems of determination of the right side and coefficients of linear differential equations and systems by their solutions -- Â2 Inverse problems for the first order linear equation with a parameter |
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Â3 Inverse problems for linear differential equations of the second order with a parameterÂ4 Inverse problems for nonlinear ordinary differential equations -- Â5 Exercises for readers -- Chapter 3. Linear inverse problems for partial differential equations -- Â1 Inverse problems for the heat conductivity equation -- Â2 Inverse problems for the vibration equation -- Â3 Inverse problems for the Laplace and Poisson equations -- Â4 Exercises for readers -- Chapter 4. Inverse coefficient problems for partial differential equations |
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Â1 Inverse problems for first order equationsÂ2 The problem of determining the coefficient of the hyperbolic equation -- Â3 Reduction of inverse coefficient problems to inverse problems for ordinary differential equations with a parameter -- Â4 The problem of determining the coefficient dependent on the solution -- Â5 Exercises for readers -- Chapter 5. Problems of determining the function from the values of integrals -- Â1 Determining the function of one variable from the integral of this function. The moment problem |
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Â2 Inversion of the Radon transformation. The problems of computer tomographyÂ3 Determining the function of two variables from its integrals along the circles -- Â4 Exercises for readers -- Chapter 6. Methods of solution of inverse problems -- Â1 Solving equations of the first kind on compact sets. The quasisolution method -- Â2 The Tikhonov regularization method -- Â3 The iterative method of solving equations of the first kind -- Â4 The projective method for solving equations of the first kind |
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Â5 Methods for solving Fredholm integral equations of the first kindÂ6 Method of solution of the Volterra integral equation of the first kind -- Â7 The quasi-inversion method -- Â8 Exercises for readers -- Bibliography |
Bibliography |
Includes bibliographical references |
Notes |
Online resource; title from PDF title page (ebrary, viewed February 12, 2015) |
Subject |
Inverse problems (Differential equations)
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Inverse problems (Differential equations)
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Form |
Electronic book
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ISBN |
9783110943252 |
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3110943255 |
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