This paper develops a tensor-structured asynchronous least-squares progressive-iterative approximation method (ALSPIA) for least-squares fitting and reconstruction of incomplete tensor-product B-spline surface data. A binary mask matrix is introduced to impose fitting constraints only on the observed entries. The resulting matrix-form iteration is algebraically equivalent to applying ALSPIA to the vectorized least-squares system containing only the observed data. However, it avoids explicitly constructing the row-restricted Kronecker-product collocation matrix and retains the original two-dimensional tensor-product representation. The convergence properties of the proposed tensor-structured implementation are analyzed for both singular and nonsingular weighted normal matrices. Numerical experiments with different missing-data patterns demonstrate the effectiveness of the method for surface reconstruction.
Citation: Xianglan Ge, Lijuan Hu. On a weighted ALSPIA method for tensor-product B-spline surface fitting with missing data[J]. AIMS Mathematics, 2026, 11(9): 30437-30459. doi: 10.3934/math.20261206
This paper develops a tensor-structured asynchronous least-squares progressive-iterative approximation method (ALSPIA) for least-squares fitting and reconstruction of incomplete tensor-product B-spline surface data. A binary mask matrix is introduced to impose fitting constraints only on the observed entries. The resulting matrix-form iteration is algebraically equivalent to applying ALSPIA to the vectorized least-squares system containing only the observed data. However, it avoids explicitly constructing the row-restricted Kronecker-product collocation matrix and retains the original two-dimensional tensor-product representation. The convergence properties of the proposed tensor-structured implementation are analyzed for both singular and nonsingular weighted normal matrices. Numerical experiments with different missing-data patterns demonstrate the effectiveness of the method for surface reconstruction.
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Xianglan Ge, Lijuan Hu. On a weighted ALSPIA method for tensor-product B-spline surface fitting with missing data[J]. AIMS Mathematics, 2026, 11(9): 30437-30459. doi: 10.3934/math.20261206
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