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Elements of the theory of inverse problems /

Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Denisov, A. M. (Autor)
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Utrecht, the Netherlands : VSP, 1999.
Colección:	Inverse and ill-posed problems series.
Temas:	Inverse problems (Differential equations) Problèmes inverses (Équations différentielles) MATHEMATICS > Calculus. MATHEMATICS > Mathematical Analysis.
Acceso en línea:	Texto completo

Tabla de Contenidos:

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
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
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
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
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

Elements of the theory of inverse problems /

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