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首页> 外文期刊>Applied mathematics and computation >Determination of leading coefficients in Sturm-Liouville operator from boundary measurements. I. A stripping algorithm
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Determination of leading coefficients in Sturm-Liouville operator from boundary measurements. I. A stripping algorithm

机译：通过边界测量确定Sturm-Liouville算子中的前导系数。一，剥离算法

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摘要

We present a stripping algorithm for determination of the unknown coefficient k = k(x) in the Sturm-Liouville operator Au = (k(x)u'(x))' + q(x)u(x), x is an element of (a, b), form boundary measurements. Due to the only two physically possible measured data at the boundary, the problem is of strong unstable. The formulation of the problem based on the Tikhonov's quasisolution approach. The coefficient k(x) is an element of L-2[a, b] is assumed to be a monotone and uniform bounded function. This class of functions K-c is compact in L-2[a, b] and hence the inverse problem has at least one quasisolution in K-c. The stripping algorithm is implemented for the cases, when the unknown function k(x) is interpolated by the first- and second-order polynomials. Effectiveness of the method is demonstrated on concrete numerical examples with exact and noisy data. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 8]
机译：我们提出一种剥离算法，用于确定Sturm-Liouville算子中的未知系数k = k（x）Au =（k（x）u'（x））'+ q（x）u（x），x是一个（a，b）的元素，形成边界测量。由于边界上仅有两个物理上可能的测量数据，因此该问题非常不稳定。根据Tikhonov的拟解方法制定问题。系数k（x）是L-2 [a，b]的元素，被假定为单调且有界函数。这类函数K-c在L-2 [a，b]中很紧凑，因此反问题在K-c中至少具有一个拟解。当未知函数k（x）由一阶和二阶多项式插值时，将采用剥离算法。该方法的有效性在具有精确和嘈杂数据的具体数值示例上得到了证明。 （C）2002 Elsevier Science Inc.保留所有权利。 [参考：8]

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