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Start Over Topic 01 natural sciences Topic applied mathematics Topic general mathematics Journal bulletin of the australian mathematical society Publisher cambridge university press (cup)
2 results

1. BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES

Author

Qing-Ge Kong, Huo-Jun Ruan, and Sheng Zhang

Subjects
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.

Published
2018

2. A MODIFIED FR CONJUGATE GRADIENT METHOD FOR COMPUTING -EIGENPAIRS OF SYMMETRIC TENSORS

Author

Guanghui Zhou and Meilan Zeng

Subjects
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