## Solutions of ill-posed problems |

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### Contents

INTRODUCTION | 1 |

THE SELECTION METHOD QUASISOLUTIONS | 27 |

THE REGULARIZATION METHOD | 45 |

Copyright | |

10 other sections not shown

### Common terms and phrases

A. N. Tikhonov Af(co approximate solution asymptotic belongs Chapter compact set constructing converges convolution type corresponding denote determined deviation discrepancy element z0 error estimate exact solution example exists finding an approximate formula Fourier series Fredholm integral equation function z(s functional J2[z given greatest lower bound Hilbert space ill-posed problems initial data integral equation lemma Let us look Let us suppose linear algebraic Ma[z matematicheskoy fiziki mathematical metric space minimizing sequence minimizing the functional nonnegative normal solution obtain Obviously operator for equation operator R(u optimal control positive number problem of finding problem of minimizing pth-order stabilizers regularization method regularization parameter regularized solution regularizing operator right-hand member u(x set F small changes smoothing functional solution of equation solution zT(t space F spectral density stabilizing factors stabilizing functional stable method stable under small target function Theorem unique uT(t vector well-posed Wiener filtering za(t zero