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In this paper, we propose a novel rank-adaptive higher-order orthogonal iteration (RA-HOOI) algorithm to solve the fixed-accuracy low multilinear-rank approximation of tensors. On the one hand, RA-HOOI relies on a greedy strategy to expand the subspace, which avoids computing the full SVD of the matricization of the input tensor. On the other hand, the new rank-adaptive strategy introduced in the RA-HOOI algorithm enables the obtained truncation to be more accurate. A series of numerical experiments related to synthetic and real-world tensors are carried out to show that the proposed RA-HOOI algorithm is comparable to state-of-the-art methods in terms of both accuracy and efficiency and performs better in certain situations. [ABSTRACT FROM AUTHOR]

A large interval of random perturbation is presented in this study. Under the derived interval, the probability that the simple eigenvalue of original symmetric matrix is still simple is not less than a given confidence level. Numerical examples are provided to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, some new absolute perturbation bounds of partitioned generalized Hermitian positive definite eigenvalue problem are established by two different ways. Numerical results show that our bounds are sharper than the ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, by transforming the symmetric random perturbed matrix into a special form and using the result from Li and Li (2005) [7] , we first present an improved random perturbation interval. Under the random perturbation in the interval, the simple eigenvalue of the original matrix is still simple. Then, we extend the result to the case of several eigenvalues. Finally, numerical experiments are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

• The refractive index of the film decreases 0.02–0.08 after irradiation. • The film after irradiation exhibits 2% photo-expansion. • The refractive index change and photo-expansion remain a linear relationship. • The photo-expansion is the main reason for the decrease of the refractive index. • The refractive index decrease is related to a less connected glass network. Femtosecond (fs) laser-induced functional microstructure in transparent chalcogenide film has potential application value in the field of novel infrared micro-nano photonic devices. Refractive index and thickness control of the film are crucial to manufacture infrared photonic devices. However, the changes of the refractive index and thickness induced by fs laser are too tiny to be characterized. In this condition, we designed and developed a method for studying the influencing factors of small refractive index changes induced by fs laser irradiation process. We obtained 64 different modified regions in chalcogenide film by using the laser direct writing technology. The transmission spectra of these fs laser-modified regions were recorded by use of micro-FTIR spectrometer. The refractive index and thickness of the transparent film before and after irradiation were calculated by an improved Swanepoel method. The dependence of the refractive index variation and the photo-expansion in the chalcogenide film on irradiation parameters (laser power and stage translational speed) was obtained quantitatively for the first time as far as our knowledge. The results show that the transparent chalcogenide film exhibits expansion and decreasing refractive index after fs laser irradiation. The transition threshold from non-thermal to thermal has been estimated for the Ge 20 Sb 15 Se 65 film to be ~15.6 GW/cm2. There is a linear relationship between refractive index change and photo-expansion around the threshold. Raman spectroscopy analysis of the modified area suggests that the change of refractive index and thickness may be due to the reduction in glass network connectivity of the Ge-based film induced by fs laser. [ABSTRACT FROM AUTHOR]

The translation matching method (TMM) was presented here to obtain the refractive index (RI) of chalcogenide films more accurately. It solved the problem of calculation errors of the RI of the film that resulted from using the Swanepoel method after conventional treatments such as illumination, electrical measurement, and annealing. The TMM was suitable for calculating the RI of the film by calibrating the transmission spectrum regardless of whether it had been dealt with. The accuracy of the RI calculation is about 0.1% using the method. Experimentally, the method was used to obtain the RI of three chalcogenide films: they are original homogeneous film and RI nonuniform film treated by annealing and by femtosecond laser direct writing, respectively. The results showed that the decrease in the transmittance and weakened interference effect were effectively overcome and the RI of the three kinds of films was accurately obtained by using the method. This work should provide a useful guideline for obtaining the RI of the transparent optical films. [ABSTRACT FROM AUTHOR]

The germanium antimony selenide (Ge-Sb-Se) film has emerged as an appealing infrared material with good photosensitivity, large nonlinear coefficient and high transmittance in infrared region. In particular, an infrared optical motherboard can be fabricated in the film by femtosecond (fs) laser micromachining. A detailed quantitative structural and optical characterization for 36 different regions in the film induced by fs laser is reported. By adjusting the laser power and scanning speed, different induced regions in chalcogenide films were obtained by laser direct writing. The size of the focused spot was about 0. 3 μ m which was consistent with the distance between two adjacent lines fabricated into the Ge-Sb-Se film with the thickness of 1. 4 μ m. The refractive index of the film was obtained by using the improved Swanepoel method with an accuracy of better than 0.1%. The transmittance, refractive index, absorption coefficient and optical band gap as a function of the power density were obtained. The results showed that the transmittance, refractive index and optical band gap of the film decreased, while the absorption coefficient increased with the increase of laser power and the decrease of translation velocity gradually. Raman spectroscopy indicated that the Ge–Ge bonds in the Ge 2 Se 6∕2 ethane structure and the Se–Se homopolar bonds in Se μ long chain or in the Se 8 ring were reduced after laser irradiation, and more edge-sharing GeSe 4 tetrahedral structures were formed which resulted in the refractive index change of the film. This work should provide a useful guideline for the preparation of versatile photonic devices based on Ge-Sb-Se films. • The interaction between focused 800 nm femtosecond laser and Ge-Sb-Se film was investigated quantitatively. • The optical band gap decreases and the absorption coefficient increases after laser irradiation. • The film after laser irradiation exhibits 2% photo-expansion and the refractive index of the film decreases 0.01–0.08. • The refractive index change and photo-expansion remain a linear relationship. [ABSTRACT FROM AUTHOR]