Solutions of ill posed problems

Contents......Page all_12892_to_00272.cpc0003.djvu
Translation Editor's Preface......Page all_12892_to_00272.cpc0007.djvu
Preface to the English Edition......Page all_12892_to_00272.cpc0009.djvu
1. Remarks on the formulation of mathematical problems......Page all_12892_to_00272.cpc0013.djvu
2. The concepts of well-posed and ill-posed problems......Page all_12892_to_00272.cpc0019.djvu
3. Examples of ill-posed problems......Page all_12892_to_00272.cpc0021.djvu
I. The Selection Method. Quasisolutions......Page all_12892_to_00272.cpc0039.djvu
1. The selection method of solving ill-posed problems......Page all_12892_to_00272.cpc0040.djvu
2. Quasisolutions......Page all_12892_to_00272.cpc0044.djvu
3. Approximate determination of quasisolutions......Page all_12892_to_00272.cpc0049.djvu
4. Replacement of the question Az = u with an equation close to it......Page all_12892_to_00272.cpc0052.djvu
5. The method of quasiinversion......Page all_12892_to_00272.cpc0054.djvu
1. The concept of a regularizing operator......Page all_12892_to_00272.cpc0057.djvu
2. Methods of constructing regularizing operators......Page all_12892_to_00272.cpc0062.djvu
3. The construction of regularizing operators by minimization of a smoothing funcational......Page all_12892_to_00272.cpc0075.djvu
4. Application of the regularization method to the approximate solution of integral equations of the first kind......Page all_12892_to_00272.cpc0085.djvu
5. Examples of application of the regularization method......Page all_12892_to_00272.cpc0090.djvu
6. Determination of the regularization parameter......Page all_12892_to_00272.cpc0099.djvu
III. Solution of Singular and Ill-Conditioned Systems of Linear Algebraic Equations......Page all_12892_to_00272.cpc0107.djvu
1. The regularization method of finding the normal solution......Page all_12892_to_00272.cpc0111.djvu
2. Supplementary remarks......Page all_12892_to_00272.cpc0119.djvu
IV. Approximate Solutions of Integral Equations of the First Kind of the Convolution Type......Page all_12892_to_00272.cpc0121.djvu
1. Classes of regularizing operators for equations of the convolution type......Page all_12892_to_00272.cpc0124.djvu
2. Deviation of the regularized solution from the exact one......Page all_12892_to_00272.cpc0138.djvu
3. Asymptotic estimates of the deviation of a regularized solution from the exact solution for an equation of the convolution type as a --> 0......Page all_12892_to_00272.cpc0143.djvu
V. Certain Optimal Regularizing Operators for Integral Equations of the Convolution Type......Page all_12892_to_00272.cpc0161.djvu
1. The optimal regularized solution. The connection between the regularization method and optimal Wiener filtering......Page all_12892_to_00272.cpc0163.djvu
2. Properties of the function \psi(p) for equations with kernels of types I-IV......Page all_12892_to_00272.cpc0169.djvu
3. Determination of the high-frequency characteristics of a signal and noise and of the optimal value of the regularization parameter......Page all_12892_to_00272.cpc0178.djvu
VI. Stable Methods of Summing Fourier Series With Coefficients that Are Approximate in the l_2 Metric......Page all_12892_to_00272.cpc0189.djvu
1. Classes of stable methods of summing Fourier series......Page all_12892_to_00272.cpc0191.djvu
2. Optimal methods of summing Fourier series......Page all_12892_to_00272.cpc0201.djvu
VII. Stable Methods of Minimizing Functionals and Solving Optimal Control Problems......Page all_12892_to_00272.cpc0205.djvu
1. A stable method of minimizing functionals......Page all_12892_to_00272.cpc0208.djvu
2. A stable method of solving optimal-control problems......Page all_12892_to_00272.cpc0216.djvu
VIII. Stable Methods of Solving Optimal-Planning (Linear-Programming) Problems......Page all_12892_to_00272.cpc0225.djvu
1.The formulation of optimal-planning and mathematical-programming problems......Page all_12892_to_00272.cpc0226.djvu
2. Optimal-planning problems. Existence and uniqueness of solutions......Page all_12892_to_00272.cpc0230.djvu
3. The regularization method of solving optimal-planning problems......Page all_12892_to_00272.cpc0236.djvu
Bibliography......Page all_12892_to_00272.cpc0250.djvu
Subject Index......Page all_12892_to_00272.cpc0270.djvu