G Power Software Citation
Billie Kjergaard
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Brief description of the issue:
Since Sim Update 5, the Cessna Citation Longitude has very little power. I was able to take off from KLAS Las Vegas International Airport, but in route at full throttle, I struggled to get above 300 knots.
I first tried from cold iron and pressed Ctrl E to start the engine. Then after realizing I had no power and going back to the main menu and started over on the runway at KLAS with the engine running. I assume the fuel valve would be open, but I will double check. Thank you for the suggestions.
Scince last update in cessna longitude C700 the middle screen do not display it is important to get this screen all info like engine, flap, apu, speed brake and all warning is on thid display.and throttle do not work at all.
What is the right citation for the power iteration method to find eigenvalues, if I want to cite the method in a paper? I've seen some Google PageRank references in this context. But Brin and Page didn't invent the power iteration method, did they?
Householder called this Simple Iteration, and attributed the first treatment of it to Mntz (1913). Bodewig attributes the power method to von Mises, and acknowledges Mntz for computing approximate eigenvalues from quotients of minors of the explicitly computed matrix $A^k$ , for increasing values of $k$.
In 1913 he published two notes in Comptes Rendus in connection with the use of iterative techniques for the solutions of algebraic equations. It is very possible that Mntz was the first to develop an iterative procedure for the determination of the smallest eigenvalue of a positive definite matrix. It certainly predates the more generally quoted result of R. von Mises of 1929.
Mntz's real innovation in the first one of his 1913 papers is the method of simultaneous or orthogonal iteration: "Qu'on parte des n directions consecutives ...; en orthogonalisant et en normant, d'apres les notations connues de M. Schmidt, les determinants, on obtiendra convergence ... vers les axes principaux, en general toutes les n."
In his Ph.D. thesis Erhard Schmidt proved the existence of an eigenfunction of a symmetric integral operator by using iterated kernels, the equivalent of matrix powers in a function space. In order to avoid convergence problems in the case of eigenvalues of equal modulus, he did not apply the integral operator directly to a function.
In his 1909 textbook "Determinantentheorie" Gerhard Kowalewski, a distant relative of Kovalevskaya's husband, gave a finite-dimensional version of Schmidt's existence proof for a symmetric matrix T, and then proposed "a simple infinite process to get to an invariant of T", the power method.
I vaguely remember, that this is due to Hotelling (1933). I don't have the monography of S. Mulaik "The foundations of factor analysis" (1972) at hand, but google-books let's you have a peek for "Hotelling". At page 114/115 this is discussed and Mulaik writes: "However, in 1933 Hotelling published a paper in the Journal of Educational Psychology which described a method of finding the characteristic equation directly (...)" Page 115: "(...) permitting us thereby to pick from among the eigenvectors the one associated with the largest eigenvalue. As a matter of fact, both kinds of methods are available. The first, which converges to the eigenvector associated with the largest eigenvalue, is due to Hotelling.(...)"
The method named after Jacobi to find the eigenvalues/eigenvectors is the special case of rotating the columns of a matrix to approximate a certain maximization criterion iteratively. This can be done if a symmetric matrix was decomposed for instance in its two triangular cholesky-factors, and the lower triangular factor is ("Jacobi"-) rotated to "principal components position". Here all pairs of columns are rotated to maximize some criterion and this is repeated until some convergence criterion is satisfied (I can provide that criterion if needed because I've implemented it in a software).
The book of S. Mulaik is a bit aged and of the year 1972, and although there is a lot of modern development in factor-analysis I rate it as still the best monography/standard textbook for the basic understanding of factor analysis and related basic methods of linear algebra (as well for the history...)
G*Power is a tool to compute statistical power analyses for many different t tests, F tests, χ2 tests, z tests and some exact tests. G*Power can also be used to compute effect sizes and to display graphically the results of power analyses.
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If you use G*Power for your research, then we would appreciate your including one or both of the following references (depending on what is appropriate) to the program in the papers in which you publish your results:
Improvements in the logistic regression module: (1) improved numerical stability (in particular for lognormal distributed covariates); (2) additional validity checks for input parameters (this applies also to the poisson regression module); (3) in sensitivity analyses the handling of cases in which the power does not increase monotonically with effect size is improved: an additional Actual power output field has been added; a deviation of this actual power value from the one requested on the input side indicates such cases; it is recommended that you check how the power depends on the effect size in the plot window.
Fixed a problem in the test of equality of two variances. The problem did not occur when both sample sizes were identical.
Fixed a problem in calculating the effect size from variances in the repeated measures ANOVA.
Added an options dialog to the repeated-measures ANOVA which allows a more flexible specification of effect sizes.
Fixed a problem in calculating the sample size for Fisher's exact test. The problem did not occur with post hoc analyses.
Renamed the Repetitions parameter in repeated measures procedures to Number of measurements (Repetitions was misleading because it incorrectly suggested that the first measurement would not be counted).
Fixed a problem in the sensitivity analysis of the logistic regression procedure: There was an error if Odds ratio was chosen as the effect size. The problem did not occur when the effect size was specified in terms of Two probabilities.
The Window menu now contains the option to hide the distributions plot and the protocol section (Hide distributions & protocol menu item) so that G*Power can be accommodated to small screens. This option has been available for some time in the Windows version (see View menu).
Added procedures to analyze the power of tests for single correlations based on the tetrachoric model, comparisons of dependent correlations, bivariate linear regression, multiple linear regression based on the random predictor model, logistic regression, and Poisson regression.
Added procedures to analyze the power of tests referring to single correlations based on the tetrachoric model, comparisons of dependent correlations, bivariate linear regression, multiple linear regression based on the random predictor model, logistic regression, and Poisson regression.
Fixed a bug in the function calculating the CDF of the noncentral t-distribution that occasionally led to (obviously) wrong values when p was very close to 1. All power routines based on the t distribution were affected by this bug.
Fixed a bug in the Power Plot (opened using the X-Y-plot for a range of values button) for F tests, MANOVA: Global effects and F Tests, MANOVA: Special effects and interactions. Sometimes some of the variables were not correctly set in the plot procedure which led to erroneous values in the graphs and the associated tables.
Fixed a bug in the X-Y plots for a range of values for F Tests, ANOVA: Fixed effects, special, main effects and interactions. The df1 value was not always correctly determined in the plot procedure which led to erroneous values in the plots.
Fixed the problem in the plot procedure that (due to rounding errors) the last point on the x-axis was sometimes not included in the plot.
Added options mainly intended to make G*Power usable with low resolution displays (800 x 600 pixels)
The distribution/protocol view and the test/analysis selection view in the main window can be hidden temporarily to save space. To hide/show these sub-views press F4 (plot/protocol) and F5 (test/analysis), respectively, while the main window is active. There are also corresponding entries in the View menu.
The Graph window can now be made resizable. To do this choose "Resizable Window" in the View menu of the Graph window. Besides enabling (restricted) resizability this option initially shrinks the window to a size that fits into a 800 x 600 screen. Deselecting the option restores the Graph window to the fixed size for which G*Power was optimized.
The main aim of this paper is to use a statistically rigorous approach to answer the empirical question of whether the power-law model describes best the observed distribution of highly cited papers. We use the statistical toolbox for detecting power-law behaviour introduced by Clauset et al. (2009). There are two major contributions of the present paper. First, we use a very large, previously unused data set on the citation distributions of the most highly cited papers in several fields of science. This data set comes from Scopus, a bibliographic database introduced in 2004 by Elsevier, and contains 2.2 million articles published between 1998 and 2002 and categorized in 27 Scopus major subject areas of science. Most of the previous studies used rather small data sets, which were not suitable for rigorous statistical detecting of the power-law behaviour. In contrast, our sample is even bigger with respect to the most highly cited papers than the large sample used in the recent contributions based on WoS data (Albarrn and Ruiz-Castillo 2011; Albarrn et al. 2011a, b). This results from the fact that Scopus indexes about 70 % more sources compared to the WoS (Lpez-Illescas et al. 2008; Chadegani et al. 2013) and therefore gives a more comprehensive coverage of citation distributions.Footnote 1
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