Least-squares Fitting Method Research Articles

Generalized Rational Krylov Decompositions with an Application to Rational Approximation

Generalized rational Krylov decompositions are matrix relations which, under certain conditions, are associated with rational Krylov spaces. We study the algebraic properties of such decompositions and present an implicit Q theorem for rational Krylov spaces. Transformations on rational Krylov decompositions allow for changing the poles of a rational Krylov space without recomputation, and two algorithms are presented for this task. Using such transformations we develop a rational Krylov method for rational least squares fitting. Numerical experiments indicate that the proposed method converges fast and robustly. A MATLAB toolbox with implementations of the presented algorithms and experiments is provided.

Disk of the Small Magellanic Cloud as traced by Cepheids

The structure and evolution of the disk of the Small Magellanic Cloud (SMC) are traced by studying the Cepheids. We aim to estimate the orientation measurements of the disk, such as the inclination and the position angle of the line of nodes, and the depth of the disk. We used the V and I band photometric data of the fundamental and first-overtone Cepheids from the Optical Gravitational Lensing Experiment survey. The period-luminosity relations were used to estimate the relative distance and reddening of each Cepheid. A weighted least-square plane fitting method was then applied to estimate the structural parameters. The line-of-sight depth and then the orientation corrected depth or thickness of the disk were estimated from the relative distance measurements. The period-age-colour relation of Cepheids were used to derive the age of the Cepheids. A break in the PL relations of the fundamental-mode and first-overtone Cepheids at P ~ 2.95 days and P ~ 1 day are observed. An inclination of 64$^o$.4$\pm$0$^o$.7 and a PA$_{lon}$=155$^o$.3$\pm$6$^o$.3 are obtained from the full sample. A reddening map of the SMC disk is also presented. The orientation-corrected depth or thickness of the SMC disk is found to be 1.76 $\pm$ 0.6 kpc. The scale height is estimated to be 0.82 $\pm$ 0.3 kpc. The age distribution of Cepheids matches the SMC cluster age distribution. The radial variation of the disk parameters mildly indicate structures/disturbances in the inner SMC (0.5 $<$ r $<$ 2.5 degree). Some of the Cepheids found in front of the fitted plane in the eastern regions are possibly the youngest tidally stripped counterpart of the H {{\sc i}} gas of the Magellanic Bridge. The Cepheids behind the fitted plane are most likely the population in the Counter Bridge predicted in recent numerical simulations. Different scenarios for the origin of the extra-planar Cepheids are also discussed.

Finite element method with nonlocal boundary condition for solving the nondestructive testing problem of wood moisture content

In this paper, we use the finite element method (FEM) with nonlocal boundary condition for solving the nondestructive testing problem of wood moisture content based on a planar capacitance sensor model (i.e. the DtN-FEM for solving the mathematical model which is described by the exterior problems of a class of 3D Laplace equation with complicated boundary conditions). The original boundary value problem is reduced to an equivalent nonlocal boundary value problem via a Dirichlet-to-Neumann (DtN) mapping represented in terms of the Fourier expansion series. For numerical computation, a series of approximate problems with higher accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. The error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. Based on the numerical results, the relationship between the dielectric constant (DC) of tested wood and the capacitance value of the sensor is discussed. Finally, we applied a least squares fitting method (LSFM) to reconstruct the wood moisture content (WMC) from the data measured with a planar capacitance sensor. Compared with popular statistical methods, the hybrid experimental–computational method is more convenient and faster, and a large number of experiments are avoided, the costs of testing are reduced.

Theoretical Stark widths and shifts of spectral lines of 2p5nf and 2p55g configurations of Mg III

In this paper, we report theoretical Stark widths and shifts calculated using the Griem semi-empirical approach, which corresponds to 111 spectral lines of Mg III. The values of these Stark broadening parameters of spectral lines that arise from levels of 2p5nf and 2p55g configurations of Mg III are presented in the literature for the first time. The aim of this work is to provide values to estimate the electron density of plasma Mg III in astrophysics and industrial applications. The data are presented for the temperatures T = 0.5–10.0 (104 K) and for an electron density of 1017 cm−3. The matrix of elements used in these calculations has been determined from 23 configurations of Mg III: 2s22p6, 2s22p53p, 2s22p54p, 2s22p54f and 2s22p55f for the even parity and 2s22p5ns (n = 3–6), 2s22p5nd (n = 3–9), 2s22p55g and 2s2p6np (n = 3–8) for the odd parity. For the intermediate coupling calculations, we use the standard method of least square fitting from experimental energy levels by means of Cowan’s computer code. Lines with wavelengths of 134.6460, 135.2800, 189.0380, 190.0043, 192.8424, 408.2939 and 409.4375 nm have high probabilities and also have high values of broadening. Therefore, these lines can be used in some applications. A common regularity for the Stark width of the 189.038 nm spectral line of Mg III is discussed.

Analysis of movement axes of the ankle and subtalar joints: relationship with the articular surfaces of the talus.

Bone shape varies among human populations, and in the case of articular joints, the shape of the articulating surfaces strongly influences joint movement. In this study, we aimed to analyse the axes of the talocrural and subtalar joints, using the talar articular surface method, and compare these results with those of the previous studies. We used three-dimensional reconstruction models of tali among Korean individuals. The axes of the talocrural and subtalar joints were calculated by using the least-square sphere fitting method, and the principal axis was used for reference coordination. The shape of the talus was classified based on the shape of its anterior, middle, and posterior calcaneal facets, and the talar shape was compared with the movement axes. The movement axes did not differ according to the type of calcaneal facets of the talus. Interestingly, we also noted that the axes of the talocrural and subtalar joints in this study differed significantly from those reported in the previous studies; these differences may be due to variations in the shape of the bones.

Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface.

This paper presents a field curvature correction method of designing an ultrashort throw ratio (TR) projection lens for an imaging system. The projection lens is composed of several refractive optical elements and an odd polynomial mirror surface. A curved image is formed in a direction away from the odd polynomial mirror surface by the refractive optical elements from the image formed on the digital micromirror device (DMD) panel, and the curved image formed is its virtual image. Then the odd polynomial mirror surface enlarges the curved image and a plane image is formed on the screen. Based on the relationship between the chief ray from the exit pupil of each field of view (FOV) and the corresponding predescribed position on the screen, the initial profile of the freeform mirror surface is calculated by using segments of the hyperbolic according to the laws of reflection. For further optimization, the value of the high-order odd polynomial surface is used to express the freeform mirror surface through a least-squares fitting method. As an example, an ultrashort TR projection lens that realizes projection onto a large 50 in. screen at a distance of only 510 mm is presented. The optical performance for the designed projection lens is analyzed by ray tracing method. Results show that an ultrashort TR projection lens modulation transfer function of over 60% at 0.5 cycles/mm for all optimization fields is achievable with f-number of 2.0, 126° full FOV, <1% distortion, and 0.46 TR. Moreover, in comparing the proposed projection lens' optical specifications to that of traditional projection lenses, aspheric mirror projection lenses, and conventional short TR projection lenses, results indicate that this projection lens has the advantages of ultrashort TR, low f-number, wide full FOV, and small distortion.

Robust and accurate personalised reconstruction of standard 12-lead system from Frank vectorcardiographic system

In this article, we have proposed a robust and accurate method for the reconstruction of standard 12-lead (S12) system from Frank vectorcardiographic (FV) system using personalised transformation (PT) matrices targeting personalised remote health monitoring applications. FV system is used in the 3D visualisation of heart and diagnosis and prognosis of many cardiologic disorders including myocardial infarction, Brugada syndrome etc. However, cardiologists are accustomed to S12 system pertaining to its decades-old usage and widespread acceptability and hence, it is generally used as primary ECG acquisition system and state-of-the-art inverse Dower transform (DT) and affine transform (AT) are used to obtain FV system from S12 system. Here, we propose the acquisition of FV system and use PT to reconstruct S12 system from FV system. PhysioNet's PTB database after wavelet-based preprocessing to remove baseline wandering and noise has been used in this investigation. The personalised coefficients have been obtained using least-squares fit method and heart-vector projection theory and evaluation metrics used are R2 statistics, correlation and regression coefficients. Our proposed PT methodology has outperformed AT and DT by mean R2 values of 16.36% and 26.53%, respectively. For the practical application of the proposed system, we have investigated into the reusability of personalised coefficients which has been shown to outperform state-of-the-art AT and DT.

Measurement on Gas Number Density Distribution by Tunable Diode Laser Absorption Spectroscopy

An experimental technique was designed to measure the gas number density distribution of alkali vapor by tunable diode laser absorption spectroscopy. The measurement method was developed by scanning multiple gas absorption lines and fitting the experiment data with Lorentz profile to obtain the density. A discretization strategy of the equation for absorption lines is also present here as well as a constrained liner least-square fitting method. A simulation model was set up to reconstruct the two-dimensional distribution of number density and the feasibility of the reconstruction was verified. In the end, this work demonstrates the calculation error of the acquired number density and the distribution. The results indicated that the error would be no more than 5% if the measurement error is less than 9%.

Experimental Study of Methane Sensor Based on the Principle of Infrared Detection

This paper presents a structural design of a methane sensor based on the principle of infrared detection, and designs a program of the experimental calibration. In the conditions of laboratory, different concentrations of methane gas were detected. A concentration inversion formula was proposed by the segmented least-square fitting method. The sensor can measure concentrations of methane in a real-time and accurate way, it contains the functions that digital display and sound and light alarm. The results show that a full-scale concentrations of methane gas can be detected, when the concentration range is in 0-10%, the absolute error is less than 0.09%; when it is more than 10%, the absolute error is less than 0.2%, the response time is less than 15s.

Least-squares fitting of time-domain signals for Fourier transform mass spectrometry.

To advance Fourier transform mass spectrometry (FTMS)-based molecular structure analysis, corresponding development of the FTMS signal processing methods and instrumentation is required. Here, we demonstrate utility of a least-squares fitting (LSF) method for analysis of FTMS time-domain (transient) signals. We evaluate the LSF method in the analysis of single- and multiple-component experimental and simulated ion cyclotron resonance (ICR) and Orbitrap FTMS transient signals. Overall, the LSF method allows one to estimate the analytical limits of the conventional instrumentation and signal processing methods in FTMS. Particularly, LSF provides accurate information on initial phases of sinusoidal components in a given transient. For instance, the phase distribution obtained for a statistical set of experimental transients reveals the effect of the first data-point problem in FT-ICR MS. Additionally, LSF might be useful to improve the implementation of the absorption-mode FT spectral representation for FTMS applications. Finally, LSF can find utility in characterization and development of filter-diagonalization method (FDM) MS.

Using a pseudo-steady-state flow equation and 4D seismic traveltime shifts for estimation of pressure and saturation changes

Pressure and saturation changes cause a change in seismic P-wave velocity resulting in a shift in 4D traveltime. A discrimination between both effects is important to enhance reservoir management decisions. We explored the possibility of linking the fields of reservoir engineering and 4D seismic. A simple inversion scheme based on a reservoir engineering flow equation for pore pressure predictions combined with the Hertz-Mindlin and Gassmann rock-physics models to discriminate pressure and saturation effects from 4D time shifts was presented. To account for no-flow reservoir boundaries, the pseudo-steady-state flow equation giving the pressure distribution was extended with a superpositioning method. During the inversion, three parameters were determined by a nonlinear, least-squares fitting method: the thickness of the hydrocarbon column, the pressure at the well position, and its decay rate away from the well. We successfully tested our approach on a synthetic and a field data case, where the [Formula: see text] injection well at the Snøhvit field, Norway, served as a good example to demonstrate our method. We observed a good correlation between simulation and inversion in our synthetic study. Our theory was limited to homogeneous reservoir conditions and produces spatially low frequent outputs. To apply the model in complex fields, such as at Snøhvit, we introduced a spatially varying Mindlin-exponent over the field and used the theory as an heuristic model assuming that a variation of the Mindlin-exponent takes a change in pressure sensitivity into account. This assumption provided the possibility to indirectly include heterogeneities in grain sorting and porosity variation and improved the model significantly. We see the advantage of our method in its fast and direct implementation to study first-order effects of pressure and saturation behavior on time-lapse seismic data using a simple inversion algorithm instead of computationally intensive simulations.

Modeling of 137Cs migration in cores of marine sediments of Mumbai Harbor Bay

The vertical concentration profile of 137Cs in cores of marine sediment of Mumbai Harbor Bay has been studied by the compartment and the diffusion-convection models. Based on the measured concentrations of 137Cs in the sediment layers, the various transport parameters such as sedimentation rate, residence half- time, effective migration velocity, diffusion coefficient and the convective velocities were determined. The sedimentation rate was determined to be 1.61, 1.03 0.69 and 1.25 cm year−1 from the slope of lines obtained from the depth profile of 137Cs in cores using a least-square fitting method at site 1, 2, 3 and 4 respectively. The mean residence half-times, ranging from 11 to 35 years were observed to be the highest at the upper layers (up to 8 cm) of all sites and decreased with sediment depth. Subsequently, the ranges of mean value of effective vertical migration velocity in the same layers were between 0.15 and 0.46 cm year−1. As expected, the vertical migration in the upper sediment layers was very slow and thereafter increased slowly in the succeeding layers (12 cm onwards) of all sites with a mean ranging from 1.11 to 4.13 cm year−1. The obtained migration velocities were quite higher than those reported in literatures for global fallout. The convective velocity and diffusion coefficient at each site were assumed to be constant in the whole depth and calculated under the assumption of steady state. Using a depth-zoned bioturbational mixing model, the estimated biological diffusion coefficients ranged from 7 × 10−7 to 3.8 × 10−6 cm2 s−1 which were within the literature values reported for shallow coastal environments and deep sea.

The Approach of Error Calibration for Three-axis Magnetic Heading Sensor

The accuracy of magnetic heading sensor is reduced by the impact of manufacturing technology and local magnetic interferences. The singularity of constraint matrix in traditional calibration algorithm leads to unstable results. Therefore, an improved least-square ellipsoid fitting method is proposed in this paper. The error source and the deviation mathematical model are introduced. On the basis of the analysis on singularity of the constraints matrix, parameter extraction by the improved least-square ellipsoid fitting method is given. The new method successfully overcomes the instability of the traditional algorithm, and reduces the computation load. Simulation and experimental results show that this method is effective in calibrating magnetic heading sensor. The heading precision of the sensor acquired after calibration is better than 0.42o DOI : http://dx.doi.org/10.11591/telkomnika.v12i4.4837

Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters.

液晶显示全局动态调光算法的高效实现方法研究

The dynamic dimming algorithm consists of two steps:dimming level determination and LC pixel compensation.Look-up-table method is applied in S-curve dimming algorithm based on image classification.In order to solve the shortcomings of large consumption of hardware resources and slow processing speed of this algorithm,this paper proposes two kinds of algorithm implementations:Arithmetic Sequence Method(ASM)and Least-squares Fitting Method(LSFM).The simulation results show that the largest standard deviation is 1.8and 0.8of ASM and LSFM,respectively.The practical tests have done on the LCD TV prototype.Compared to the luminance of pixels from look-up table method,the deviation of ASM is less than 3graylevels and the deviation of LSFM is less than 1 gray-level.The hardware storage resource decreases from 71% of the proposed methods to 4% of look-up-table.The simulation and experimental results show that LSFM is better.

Some Aspects of Multiparticle Production in Relativistic Nuclear Collisions

An attempt is made to study various types of multiplicity distributions and multiplicity correlations amongst secondary charged particles produced in 4.5 and 14.5 A GeV/c 28Si-nucleus interactions. The results reveal that multiplicity correlations of the type , where i, j = b, g, s and h with i ≠ j, are linear. The observed multiplicity correlations are nicely fitted by the method of least squares fitting of the type, = b + ani. Furthermore, the multiplicity distributions of relativistic charged particles and compound multiplicity at 4.5 A GeV/c are nicely fitted by Poisson distributions with peaks at relatively lower multiplicities. However, in the case of multiplicity distributions of various types of secondary charged particles produced in 14.5 A GeV/c 28Si-nucleus collisions definite trends are not discernible.

The characteristics of excited states for HF+ ion under spin-orbit coupling

The characteristics of ground state X2Πi and the first excited state A2Σ+ of HF+ under spin-orbit coupling are studied by using the multi-configuration quasi-degenerate perturbation theory. The vertical excited energy is v[2Π1/2 (v = 0)→ X2Π3/2(v = 0)] = 285.176 cm-1, and the potential energy curves of the splitting electronic states X2Π3/2, 2Π1/2 of X2Πi are obtained. The analytical potential functions of these states are derived by employing the Murrell- Sorbie function (M-S) and the least-square fitting method, and then the spectroscopic constants for X2Π3/2, 2Π1/2 and A2Σ+ are derived from the M-S function. All the spectroscopic data and the analytical potential functions for states X2Π3/2 and 2Π1/2 are given for the first time in our calculation.

Influence of frequency and saturation on AVO attributes for patchy saturated rocks

Partially saturated rocks are considered to be major sources of seismic wave velocity dispersion and attenuation in recorded real data. From the physical description of partially saturated gas-water and oil-water reservoirs, we use upscaling theories to compute an equivalent frequency-dependent porous medium. These homogenization methods are associated with mesoscale description of attenuation and dispersion coming from wave-induced flow phenomena. To compute wave propagation, we use numerical codes in the frequency domain that allow us to take into account all the frequency-dependent parameters without approximation or local time steps. In this way, the Biot slow compressional wave is well modeled and its partially diffusive, partially propagative behavior is completely considered. The attenuation and dispersion of the waves in such media are coming partly from the wave mode conversion into diffusive slow waves, not visible on seismograms. But the amplitude of propagative P- and S-waves are mainly affected by these energy losses at interfaces. Using full waveform modeling, we investigate the amplitude versus offset (AVO) attributes with respect to saturation and frequency. For a simple three-layer case, we compute poroelastic wave propagation, extract maximum amplitude with respect to angle, and, through a least-square fitting method, we obtain the AVO attributes for PP- and PS-reflected events. Due to the influence of mesoscale induced-flow phenomena and relatively to the regime of the Biot slow wave, the main results show a strong variability of the AVO attributes with the frequency and a lower variability with the saturation for reflected PP or PS events. We show that gas-water and oil-water systems have similar behaviors. Strong differences between patchy saturation and effective fluid phase theories are highlighted, especially at high frequency, for PP events and for gas-water systems. Then, we conclude that these AVO attributes carry information about the saturation that can be used to estimate the saturation variations in time-lapse studies.

Electron microscopy analysis of Ti-substituted Li2MnO3 positive electrode before and after carbothermal reduction

40%-titanium substituted Li2MnO3 (Li1+x(Ti0.4Mn0.6)1−xO2, 0 < x < 1/3) before and after carbothermal reduction was characterized by annular dark field scanning transmission electron microscopy (ADF-STEM) and electron energy-loss spectroscopy (EELS) to investigate the effects of the pre-reduction treatment. EELS spectra with high energy resolution using monochromator clearly reveal the appearance of reduced Mn ions after the reduction process. The spatial distribution of the reduced phase was visualized by multi-linear least-squares (MLLS) fitting method using Mn L-edge energy-loss near-edge structure (ELNES). The morphology change of a primary particle was observed around the Mn reduction phase.

Analysis and modeling of aerothermal radiation based on experimental data

The effect of aerothermal radiation on the performance of an airborne infrared imaging system is becoming a crucial issue in the development of electro-optic systems. In this paper the high-temperature radiation characteristics of infrared window are studied in depth, and a multi-scale analysis model of aerothermal radiation degraded images is presented. The presented model adopted a least-squares fitting method to simulate the salient characteristics of the aerothermal radiation degraded images. The aerothermal radiation degradation characteristic database containing characterizing parameters of degraded images was created. Through optimization selection, the characterizing parameters were used to correct the degraded images in the real aerothermal environment. The experimental results show that the model is effective in the aerothermal radiation degraded image correction, and improves the quality of the aerothermal radiation degraded image.