Summary.The inverse Sturm-Liouville problem is the problem of finding a good approximation of a potential function q such that the eigenvalue problem (*) -y"+qy=2y holds on (0, n) for y(O)=y(n)=O and a set of given eigenvatues 2. Since this problem has to be solved numerically by discretization and since the higher discrete eigenvalues strongly deviate from the corresponding Sturm-Liouville eigenvalues 2, asymptotic corrections for the 2's serve to get better estimates for q. Let 2k(1
The paper studies a finite element algorithm giving approximations to the minimum-norm solution of ill-posed problems of the form Af = g, where A is a bounded linear operator from one Hubert space to another. It is shown that the algorithm is norm convergent in the general case and an error bound is derived for the case where g is in the range of A A*. As an example, the method has been applied to the problem of evaluating the second derivative / of a function g numerically. 1. Introduction. Let X and Y be real Hubert spaces and A a bounded linear operator from X into Y. The problem of determining, for given g in the range A(X)
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