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We consider an algebraic method for reconstruction of a harmonic function in the unit disk via a finite number of values of its Radon projections. The approach is to seek a harmonic polynomial which matches given values of Radon projections along some chords of the unit circle. We prove an analogue of the famous Marr’s formula for computing the Radon projection of the basis orthogonal polynomials in our setting of harmonic polynomials. Using this result, we show unique solvability for a family of schemes where all chords are chosen at equal distance to the origin. For the special case of chords forming a regular convex polygon, we prove error estimates on the unit circle and in the unit disk. We present an efficient reconstruction algorithm which is robust with respect to noise in the input data and provide numerical examples. 相似文献
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Flemming Damhus Pedersen 《Journal of Geometry》1979,13(2):133-143
Introducing in plane affine differential geometry a gable curve to a convex arc as the set of points of intersection for pairs of tangents to the convex arc at endpoints of parallel chords it is shown, that the gable curve and the midcurve for the same chords combined form a curve with a point of inflection at their meeting point P and such that the ratio of their curvatures tends to 3 at P, independent of the convex arc. 相似文献
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本文首先指出文献[1]中的一个错误,举例说明弱拟凸集的最佳逼近未必具有广义强唯一性,进而讨论两类共同逼近的强唯一性,在空间是一致凸、逼近集是共同太阳集的条件下,证明了最佳共同逼近具有广义强唯一性 相似文献