010101 applied mathematics, Constraint (information theory), Iterated function system, Fractal, Dimension (vector space), General Mathematics, 010102 general mathematics, Bilinear interpolation, Applied mathematics, 0101 mathematics, 01 natural sciences, Mathematics, Interpolation
Abstract
Bilinear fractal interpolation surfaces were introduced by Ruan and Xu in 2015. In this paper, we present the formula for their box dimension under certain constraint conditions.
Pure mathematics, 021103 operations research, General Mathematics, 0211 other engineering and technologies, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, symbols.namesake, Power iteration, Conjugate gradient method, Jacobian matrix and determinant, Convergence (routing), symbols, Symmetric tensor, Applied mathematics, 0101 mathematics, Mathematics
Abstract
This paper proposes improvements to the modified Fletcher–Reeves conjugate gradient method (FR-CGM) for computing $Z$-eigenpairs of symmetric tensors. The FR-CGM does not need to compute the exact gradient and Jacobian. The global convergence of this method is established. We also test other conjugate gradient methods such as the modified Polak–Ribière–Polyak conjugate gradient method (PRP-CGM) and shifted power method (SS-HOPM). Numerical experiments of FR-CGM, PRP-CGM and SS-HOPM show the efficiency of the proposed method for finding $Z$-eigenpairs of symmetric tensors.
Published
2016
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