Elements of the Theory of Inverse Problems
eBook - PDF

Elements of the Theory of Inverse Problems

  1. 280 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Elements of the Theory of Inverse Problems

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Information

Publisher
De Gruyter
Year
2014
Print ISBN
9789067643030
eBook ISBN
9783110943252
Topic
Mathematics
Subtopic
Functional Analysis
Index
Mathematics

Table of contents

  1. Chapter 1. The basic concepts of inverse and ill-posed problems
  2. §1 Inverse problems. The examples
  3. §2 Well-posed and ill-posed problems
  4. §3 Operator equations of the first and the second kinds
  5. §4 Some aspects of setting and solving inverse problems
  6. §5 Exercises for readers
  7. Chapter 2. Inverse problems for ordinary differential equations
  8. §1 Problems of determination of the right side and coefficients of linear differential equations and systems by their solutions
  9. §2 Inverse problems for the first order linear equation with a parameter
  10. §3 Inverse problems for linear differential equations of the second order with a parameter
  11. §4 Inverse problems for nonlinear ordinary differential equations
  12. §5 Exercises for readers
  13. Chapter 3. Linear inverse problems for partial differential equations
  14. §1 Inverse problems for the heat conductivity equation
  15. §2 Inverse problems for the vibration equation
  16. §3 Inverse problems for the Laplace and Poisson equations
  17. §4 Exercises for readers
  18. Chapter 4. Inverse coefficient problems for partial differential equations
  19. §1 Inverse problems for first order equations
  20. §2 The problem of determining the coefficient of the hyperbolic equation
  21. §3 Reduction of inverse coefficient problems to inverse problems for ordinary differential equations with a parameter
  22. §4 The problem of determining the coefficient dependent on the solution
  23. §5 Exercises for readers
  24. Chapter 5. Problems of determining the function from the values of integrals
  25. §1 Determining the function of one variable from the integral of this function. The moment problem
  26. §2 Inversion of the Radon transformation. The problems of computer tomography
  27. §3 Determining the function of two variables from its integrals along the circles
  28. §4 Exercises for readers
  29. Chapter 6. Methods of solution of inverse problems
  30. §1 Solving equations of the first kind on compact sets. The quasisolution method
  31. §2 The Tikhonov regularization method
  32. §3 The iterative method of solving equations of the first kind
  33. §4 The projective method for solving equations of the first kind
  34. §5 Methods for solving Fredholm integral equations of the first kind
  35. §6 Method of solution of the Volterra integral equation of the first kind
  36. §7 The quasi-inversion method
  37. §8 Exercises for readers
  38. Bibliography

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Yes, you can access Elements of the Theory of Inverse Problems by A. M. Denisov in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over 1.5 million books available in our catalogue for you to explore.