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Journal articles on the topic 'Schmidt analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Borchgrevink, Carl P. "Taking Issue with Lynn and Mullen's Meta-Analytic Recommendations." Journal of Hospitality & Tourism Research 22, no. 1 (February 1998): 98–101. http://dx.doi.org/10.1177/109634809802200109.

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Lynn and Mullen encourage hospitality researchers to avoid the Hunter and Schmidt approach to meta-analysis due to posited anomalous results and nonconformity with statistical convention. They cite Johnson, Mullen, and Salas in making said admonishment. Schmidt and Hunter have established that Johnson et al. make errors in applying the Hunter and Schmidt techniques; errors that produce the anomalous results. As such, Lynn and Mullen's statement warning hospitality researchers not to use the Hunter and Schmidt approach needs to be corrected. Hospitality researchers should not hesitate to use Hunter and Schmidt's approach. In fact, they should be encouraged to use the Hunter and Schmidt approach as it is an approach recommended by the National Research Council.

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2

Potapov, Denis, Anna Skripka, and Fedor Sukochev. "On Hilbert-Schmidt compatibility." Operators and Matrices, no. 1 (2013): 1–34. http://dx.doi.org/10.7153/oam-07-01.

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3

Gallardo-Gutiérrez, Eva A., and Marı́a J. González. "Exceptional sets and Hilbert–Schmidt composition operators." Journal of Functional Analysis 199, no. 2 (April 2003): 287–300. http://dx.doi.org/10.1016/s0022-1236(02)00006-x.

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4

Knyagina, V. N., and V. S. Monakhov. "Finite groups with seminormal Schmidt subgroups." Algebra and Logic 46, no. 4 (July 2007): 244–49. http://dx.doi.org/10.1007/s10469-007-0023-1.

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5

Vedernikov, V. A. "Finite groups with subnormal Schmidt subgroups." Algebra and Logic 46, no. 6 (November 2007): 363–72. http://dx.doi.org/10.1007/s10469-007-0036-9.

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6

Benmerzouk, D., and J. P. Barbot. "Observability analysis using Lyapunov-Schmidt method." IFAC Proceedings Volumes 37, no. 13 (September 2004): 1189–94. http://dx.doi.org/10.1016/s1474-6670(17)31388-5.

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7

Eberly, J. H. "Schmidt analysis of pure-state entanglement." Laser Physics 16, no. 6 (June 2006): 921–26. http://dx.doi.org/10.1134/s1054660x06060041.

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8

Stewart, G. W. "Error Analysis of the Quasi-Gram--Schmidt Algorithm." SIAM Journal on Matrix Analysis and Applications 27, no. 2 (January 2005): 493–506. http://dx.doi.org/10.1137/040607794.

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9

Barlow, Jesse L. "Block Modified Gram--Schmidt Algorithms and Their Analysis." SIAM Journal on Matrix Analysis and Applications 40, no. 4 (January 2019): 1257–90. http://dx.doi.org/10.1137/18m1197400.

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10

Kharisov, Timur. "Assessing serpentinite compressive strength using regression analysis." Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal, no. 1 (February 17, 2021): 45–53. http://dx.doi.org/10.21440/0536-1028-2021-1-45-53.

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Introduction. Today, the express method for assessing rock compressive strength using the Schmidt hammer is becoming more and more relevant and demanded. Compared to laboratory methods, measurements by this non-destructive express method result in the height of striker rebounding. The device has to be calibrated for further transition from the rebound height Hr to compressive strength in the UCS sample of the rock type under study. Research methodology included selection of hand specimen on the slopes of the Kiembai chrysotile asbestos open pit for laboratory tests. The height of striker rebounding was measured of Proceq RockShmidt Type N Schmidt hammer according to the ASTM method in local areas of exposed massif. Compressive strength of rock samples was tested in the laboratory using Wille Geotechnik servo hydraulic testing system. Research results. Based on the obtained data, an empirical formula has been established describing the dependence between compression strength of serpentinite in the UCS sample and striker height of rebounding of a Schmidt Type N hammer. The author’s results were compared to the ones obtained by the predecessors using a Schmidt Type L hammer when studying physical and mechanical properties of serpentinite in another field. The difference in the empirical formulas is due to the difference in physical and mechanical properties of serpentinite building up the deposits under consideration, as well as the difference in impact energy of the working Schmidt hammers

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11

Mendes, Cristiane A. "On factorization of Hilbert–Schmidt mappings." Journal of Mathematical Analysis and Applications 304, no. 1 (April 2005): 137–46. http://dx.doi.org/10.1016/j.jmaa.2004.09.008.

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12

PALADINI, ANDRESSA, GERVÁSIO SILVA CARVALHO, and RODNEY RAMIRO CAVICHIOLI. "Taxonomic review of Sphenoclypeana and cladistic analysis of Ischnorhinini (Hemiptera, Cercopidae, Tomaspidinae)." Zootaxa 2502, no. 1 (June 11, 2010): 24. http://dx.doi.org/10.11646/zootaxa.2502.1.2.

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Ischnorhinini currently comprises nine genera: Baetkia Schmidt, Homalogrypota Schmidt, Ischnorhina Stål, Laccogrypota Schmidt, Neosphenorhina Distant, Schistogonia Stål, Sphenoclypeana Lallemand & Synave, Tiodus Nast, and Typeschata Schmidt. A phylogenetic analysis is presented for defining the relationship between the genera and between the species of Sphenoclypeana, and this genus is revised and two new synonymies are proposed and the monophyly of Sphenoclypeana was corroborated. The data matrix comprises 47 characters: 31 relating to the external morphology, 10 to male genitalia and six to female genitalia. The analysis resulted in one cladogram with 102 steps CI = 0.50 and RI = 0.66. (Hyboscarta melichari (Monecphora cingulata Tunaima semiflava) (Schistogonia cercopoides Schistogonia sanguinea) (Neosphenorhina ocellata Neosphenorhina scombergi) (Ischnorhina unifascia (Homalogrypota interrupta Ischnorhina surinamensis) (Laccogrypota valida (Baetkia maroniensis (Baetkia compressa (Homalogrypota coccinea (Typeschata marginata (Sphenoclypeana parana Sphenoclypeana haematina))))))))

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13

Borosnyói, Adorján. "NDT ASSESSMENT OF EXISTING CONCRETE STRUCTURES: SPATIAL ANALYSIS OF REBOUND HAMMER RESULTS RECORDED IN-SITU." Engineering Structures and Technologies 7, no. 1 (December 15, 2015): 1–12. http://dx.doi.org/10.3846/2029882x.2015.1085331.

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A comparative spatial analysis of surface hardness of structural concrete is introduced. Main objective of the paper is to make a repeatability comparison of three types of the still most popular non-destructive testing devices for concrete: L-type original Schmidt rebound hammer, N-type original Schmidt rebound hammer and N-type Silver Schmidt rebound hammer. Results indicate that the surface hardness measurement uncertainty is related to the weight of the hammer mass and is apparently not related to the impact energy of the rebound hammer devices. It is observed that the measure of surface hardness for the Silver Schmidt rebound hammer (Q-value) does not have positive correlation to the original rebound index (R). Results indicate the best performance of the N-type original Schmidt rebound hammer in terms of stability and normality of data. Geostatistical analysis of the measured data (in terms of empirical semivariograms) highlights different statistical behaviour for the mechanical recording rebound hammers and for the electro-optical recording rebound hammer.

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14

Bogdanov, Yu I., N. A. Bogdanova, V. F. Lukichev, D. V. Fastovets, and A. Yu Chernyavskii. "Schmidt decomposition and analysis of statistical correlations." Russian Microelectronics 45, no. 5 (September 2016): 314–23. http://dx.doi.org/10.1134/s1063739716050036.

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15

Kobayashi, Ricardo Tadashi, and Taufik Abrão. "Stability analysis in Gram‐Schmidt QR decomposition." IET Signal Processing 10, no. 8 (October 2016): 912–17. http://dx.doi.org/10.1049/iet-spr.2016.0123.

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16

Carson, Erin, Kathryn Lund, and Miroslav Rozložník. "The Stability of Block Variants of Classical Gram--Schmidt." SIAM Journal on Matrix Analysis and Applications 42, no. 3 (January 2021): 1365–80. http://dx.doi.org/10.1137/21m1394424.

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17

Martı́nez-Morales, José L. "The Kernel Theorem of Hilbert–Schmidt operators." Journal of Mathematical Analysis and Applications 279, no. 1 (March 2003): 71–77. http://dx.doi.org/10.1016/s0022-247x(02)00391-8.

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18

Hirzallah, Omar, and Fuad Kittaneh. "Commutator Inequalities for the Hilbert–Schmidt Norm." Journal of Mathematical Analysis and Applications 268, no. 1 (April 2002): 67–73. http://dx.doi.org/10.1006/jmaa.2001.7791.

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19

Curtain, Ruth, Kalle Mikkola, and Amol Sasane. "The Hilbert–Schmidt property of feedback operators." Journal of Mathematical Analysis and Applications 329, no. 2 (May 2007): 1145–60. http://dx.doi.org/10.1016/j.jmaa.2006.07.037.

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20

Weiss, Gary. "Commutators of Hilbert-Schmidt operators I." Integral Equations and Operator Theory 9, no. 6 (November 1986): 877–92. http://dx.doi.org/10.1007/bf01202521.

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21

Zabreiko, P. P., and N. I. Shirokanova. "New existence theorems for Lyapunov-Schmidt integral equations." Differential Equations 40, no. 9 (September 2004): 1268–78. http://dx.doi.org/10.1007/s10625-005-0005-9.

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22

Mulolani, I., and M. Rahman. "Similarity analysis for natural convection from a vertical plate with distributed wall concentration." International Journal of Mathematics and Mathematical Sciences 23, no. 5 (2000): 319–34. http://dx.doi.org/10.1155/s0161171200001745.

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Steady laminar natural convection flow over a semi-infinite vertical plate is examined in this paper. It is assumed that the concentration of a species along the plate follows some algebraic law with respect to chemical reaction. Similarity solutions may then be obtained for different orders of reaction. The fundamental parameters of this problem are the Schmidt number, Sc, and reaction order,n. Numerical results, based on the fourth order Runge-Kutta method, for Schmidt number ranging from0.0to100.0and reaction order from0.0to1.5are presented. When chemical reaction occurs, diffusion and velocity domains are seen to expand out from the plate. For large values ofn, one may expect a smaller diffusion layer which, at fixed Schmidt number, is associated with increased velocity and reduced convection-layer.

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23

Armandroff, Taft E. "The Use of CCDs on Schmidt Telescopes." International Astronomical Union Colloquium 148 (1995): 20–29. http://dx.doi.org/10.1017/s025292110002162x.

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AbstractThe implementation of CCDs on Schmidt telescopes is discussed, including the capabilities of such systems and the new types of observations that they facilitate. An analysis of the demand for and use of the CCD system on the Burrell Schmidt is presented. Some examples of scientific investigations accomplished with Schmidt CCD systems are given. The future evolution of CCD capabilities on Schmidt telescopes is discussed.

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24

Pietsch, Albrecht. "Erhard Schmidt and his contributions to functional analysis." Mathematische Nachrichten 283, no. 1 (December 23, 2009): 6–20. http://dx.doi.org/10.1002/mana.200910127.

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25

Roth, Philip L. "Software Review: Hunter-Schmidt Meta-Analysis Programs 1.1." Organizational Research Methods 11, no. 1 (July 23, 2007): 192–96. http://dx.doi.org/10.1177/1094428106298972.

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26

Björck, Å., and C. C. Paige. "Loss and Recapture of Orthogonality in the Modified Gram–Schmidt Algorithm." SIAM Journal on Matrix Analysis and Applications 13, no. 1 (January 1992): 176–90. http://dx.doi.org/10.1137/0613015.

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27

Hu, Ronghui. "Multiplicity of Periodic Solutions for a Higher Order Difference Equation." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/925290.

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28

Lawson, Jimmie, and Yongdo Lim. "The least squares mean of positive Hilbert–Schmidt operators." Journal of Mathematical Analysis and Applications 403, no. 2 (July 2013): 365–75. http://dx.doi.org/10.1016/j.jmaa.2013.02.013.

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29

Hadwin, D., and T. V. Shulman. "Stability under Small Hilbert–Schmidt Perturbations for C*-Algebras." Functional Analysis and Its Applications 52, no. 3 (July 2018): 236–40. http://dx.doi.org/10.1007/s10688-018-0234-3.

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30

Paige, Christopher C., Miroslav Rozlozník, and Zdenvek Strakos. "Modified Gram-Schmidt (MGS), Least Squares, and Backward Stability of MGS-GMRES." SIAM Journal on Matrix Analysis and Applications 28, no. 1 (January 2006): 264–84. http://dx.doi.org/10.1137/050630416.

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31

Gordina, Maria. "Hilbert–Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry." Journal of Functional Analysis 227, no. 2 (October 2005): 245–72. http://dx.doi.org/10.1016/j.jfa.2005.05.011.

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32

Le, Trieu. "Hilbert–Schmidt Hankel Operators over Complete Reinhardt Domains." Integral Equations and Operator Theory 78, no. 4 (October 27, 2013): 515–22. http://dx.doi.org/10.1007/s00020-013-2103-z.

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33

Li, Zhao-Xiang, Ji Lao, and Zhong-Qing Wang. "MIXED FOURIER-LEGENDRE SPECTRAL METHODS FOR THE MULTIPLE SOLUTIONS OF THE SCHRODINGER EQUATION ON THE UNIT DISK." Mathematical Modelling and Analysis 22, no. 2 (March 18, 2017): 167–85. http://dx.doi.org/10.3846/13926292.2017.1285362.

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In this paper, we first compute the multiple non-trivial solutions of the Schrodinger equation on a unit disk, by using the Liapunov-Schmidt reduction and symmetry-breaking bifurcation theory, combined with the mixed Fourier-Legendre spectral and pseudospectral methods. After that, we propose the extended systems, which can detect the symmetry-breaking bifurcation points on the branch of the O(2) symmetric positive solutions. We also compute the multiple positive solutions with various symmetries of the Schrodinger equation by the branch switching method based on the Liapunov-Schmidt reduction. Finally, the bifurcation diagrams are constructed, showing the symmetry/peak breaking phenomena of the Schr¨odinger equation. Numerical results demonstrate the effectiveness of these approaches.

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34

Abed, Bouabdellah, Lakhdar Bouarbi, Mohamed Bouzit, and Mohamed-Kamel Hamidou. "A numerical analysis of pollutant dispersion in street canyon: influence of the turbulent Schmidt number." Przegląd Naukowy Inżynieria i Kształtowanie Środowiska 26, no. 4 (December 30, 2017): 423–36. http://dx.doi.org/10.22630/pniks.2017.26.4.41.

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Realizing the growing importance and availability of motor vehicles, we observe that the main source of pollution in the street canyons comes from the dispersion of automobile engine exhaust gas. It represents a substantial effect on the micro-climate conditions in urban areas. Seven idealized-2D building configurations are investigated by numerical simulations. The turbulent Schmidt number is introduced in the pollutant transport equation in order the take into account the proportion between the rate of momentum turbulent transport and the mass turbulent transport by diffusion. In the present paper, we attempt to approach the experimental test results by adjusting the values of turbulent Schmidt number to its corresponding application. It was with interest that we established this link for achieving our objectives, since the numerical results agree well with the experimental ones. The CFD code ANSYS CFX, the k, e and the RNGk-e models of turbulence have been adopted for the resolutions. From the simulation results, the turbulent Schmidt number is a range of 0.1 to 1.3 that has some effect on the prediction of pollutant dispersion in the street canyons. In the case of a flat roof canyon configuration (case: runa000), appropriate turbulent Schmidt number of 0.6 is estimated using the k-epsilon model and of 0.5 using the RNG k-e model.

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35

Gaponenko, A. M., and A. A. Kagramanova. "Analysis of the Stirling engine in the Schmidt approximation." Journal of Physics: Conference Series 1111 (December 2018): 012019. http://dx.doi.org/10.1088/1742-6596/1111/1/012019.

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36

Impero Abenavoli, R., M. Carlini, H. Kormanski, K. Rudzinska, and A. Sciaboni. "Nondimensional Schmidt Analysis for Optimal Design of Stirling Engines." Journal of Engineering for Gas Turbines and Power 118, no. 1 (January 1, 1996): 8–14. http://dx.doi.org/10.1115/1.2816555.

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General directions for rough optimal calibration of Stirling machines can be given by a non-dimensional Schmidt model (nDSM). Since different relative parameters and performance indices have been analyzed by nDSM models, there is lack of uniform conclusions in the literature. This paper describes a new nDSM of six parameters and compares four performance indices as functions of relative parameters. Two optimization tasks of two and five parameters are formulated and solved using the nDSM. Maximized criterion is cycle work per unit of mean pressure and total swept volume. An optimization code based on the algorithm of conjugate gradients with projection on linear constraints is described. The optimal values of volume phase angle, nondimensional swept volume, and dead volume are presented for different constraints imposed on temperature ratio and relative dead volumes.

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37

Klotz, L. "An Interpolation Problem for Hilbert-Schmidt Operator-Valued Stationary Processes." Zeitschrift für Analysis und ihre Anwendungen 20, no. 2 (2001): 525–35. http://dx.doi.org/10.4171/zaa/1029.

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38

Matos, Mário C. "On a Question of Pietsch about Hilbert–Schmidt Multilinear Mappings." Journal of Mathematical Analysis and Applications 257, no. 2 (May 2001): 343–55. http://dx.doi.org/10.1006/jmaa.2000.7351.

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39

DU, DONGYUN, and YUN TANG. "BIFURCATION ANALYSIS OF DIFFERENTIAL-DIFFERENCE-ALGEBRAIC EQUATIONS." International Journal of Bifurcation and Chaos 14, no. 08 (August 2004): 2853–65. http://dx.doi.org/10.1142/s0218127404010886.

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The dynamics of differential-difference-algebraic equations is studied. The paper extends the study of the local bifurcations to transcritical and pitchfork bifurcation under certain nondegenerate conditions using Lyapunov–Schmidt reduction. Furthermore, an improved version of singularity induced bifurcation theorem is given in this paper.

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40

Vorobyev, S. V., I. A. Khripun, N. A. Kuzmenko, E. M. Streltsova, and E. Y. Petrovskaya. "Schmidt syndrome in clinical practice." South Russian Journal of Therapeutic Practice 1, no. 2 (September 15, 2020): 88–92. http://dx.doi.org/10.21886/2712-8156-2020-1-2-88-92.

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The analysis of this clinical case is devoted to the need for strategic forecasting in the diagnosis of endocrine diseases. Autoimmune aggression is not directed against one organ, the progression of autoimmune damage is often slow, which increases the chances of missing a disease, and sometimes leads to a diagnosis at the time of crisis and decompensation. With timely suspicion of autoimmune polyglandular syndromes, the appointment of the necessary screening 1 time in 2-3 years, as well as patient education, we save them from years of diagnostic research, and timely compensatory therapy significantly improves the quality of life of patients.

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41

Ferrick, M. G., and K. J. Claffey. "Vector analysis of ice-fabric data." Journal of Glaciology 39, no. 132 (1993): 292–302. http://dx.doi.org/10.1017/s0022143000015951.

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Abstract The mechanical properties of ice are strongly affected by crystal texture and c-axis alignment. In this paper, we develop a general quantitative method for analysis of uniaxial crystal-orientation data. These data are represented as unit vectors from the origin with end points on the surface of a unit sphere. An orthogonal least-squares error measure is used to develop equations that define the closest plane and line through the data. The resulting eigenvalue problem is identical to that obtained by other investigators using different methods. However, here we identify an implicit assumption in the method, and observe that the error measure represents physical distance and quantifies the goodness of fit to the data of idealized structures. Also, a method is developed to transform the data and the results for viewing on Schmidt nets drawn in the best plane and the predominant basal plane of a sample, in addition to the standard xy-plane. Applications of the analysis to sea-ice samples include both numerical and Schmidt-net presentations of results.

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42

Ferrick, M. G., and K. J. Claffey. "Vector analysis of ice-fabric data." Journal of Glaciology 39, no. 132 (1993): 292–302. http://dx.doi.org/10.3189/s0022143000015951.

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AbstractThe mechanical properties of ice are strongly affected by crystal texture and c-axis alignment. In this paper, we develop a general quantitative method for analysis of uniaxial crystal-orientation data. These data are represented as unit vectors from the origin with end points on the surface of a unit sphere. An orthogonal least-squares error measure is used to develop equations that define the closest plane and line through the data. The resulting eigenvalue problem is identical to that obtained by other investigators using different methods. However, here we identify an implicit assumption in the method, and observe that the error measure represents physical distance and quantifies the goodness of fit to the data of idealized structures. Also, a method is developed to transform the data and the results for viewing on Schmidt nets drawn in the best plane and the predominant basal plane of a sample, in addition to the standard xy-plane. Applications of the analysis to sea-ice samples include both numerical and Schmidt-net presentations of results.

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43

CORRÊA, F. J. S. A., J. V. GONCALVES, and ANGELO RONCALLI. "ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS." Analysis and Applications 08, no. 02 (April 2010): 185–97. http://dx.doi.org/10.1142/s0219530510001576.

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We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.

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44

Zheng, Wenming. "Class-Incremental Generalized Discriminant Analysis." Neural Computation 18, no. 4 (April 1, 2006): 979–1006. http://dx.doi.org/10.1162/neco.2006.18.4.979.

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Generalized discriminant analysis (GDA) is the nonlinear extension of the classical linear discriminant analysis (LDA) via the kernel trick. Mathematically, GDA aims to solve a generalized eigenequation problem, which is always implemented by the use of singular value decomposition (SVD) in the previously proposed GDA algorithms. A major drawback of SVD, however, is the difficulty of designing an incremental solution for the eigenvalue problem. Moreover, there are still numerical problems of computing the eigenvalue problem of large matrices. In this article, we propose another algorithm for solving GDA as for the case of small sample size problem, which applies QR decomposition rather than SVD. A major contribution of the proposed algorithm is that it can incrementally update the discriminant vectors when new classes are inserted into the training set. The other major contribution of this article is the presentation of the modified kernel Gram-Schmidt (MKGS) orthogonalization algorithm for implementing the QR decomposition in the feature space, which is more numerically stable than the kernel Gram-Schmidt (KGS) algorithm. We conduct experiments on both simulated and real data to demonstrate the better performance of the proposed methods.

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45

Wilson, James B. "Optimal algorithms of Gram–Schmidt type." Linear Algebra and its Applications 438, no. 12 (June 2013): 4573–83. http://dx.doi.org/10.1016/j.laa.2013.02.026.

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46

Alexandersson, Per, and Boris Shapiro. "Around a multivariate Schmidt–Spitzer theorem." Linear Algebra and its Applications 446 (April 2014): 356–68. http://dx.doi.org/10.1016/j.laa.2014.01.005.

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47

Rychłewska, Urszula, Derek J. Hodgson, Halina Grabarczyk, Bohdan Drożdż, Włodzimierz M. Daniewski, Wojciech Kroszczyṅski, Miloš Buděšínský, and Miroslav Holub. "Sesquiterpene lactones of Urospermum dalechampii SCHMIDT." Collection of Czechoslovak Chemical Communications 51, no. 8 (1986): 1698–709. http://dx.doi.org/10.1135/cccc19861698.

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In the species Urospermum dalechampii SCHMIDT urospermal A (I) and 11βH,13-dihydrourospermal A (II) were detected. The latter compound was also detected in U. picroides SCHMIDT. The spectral characteristics of both lactones were completed by 13C NMR data. The structure of 11βH,13-dihydrourospermal A (II) was also confirmed by X-ray analysis.

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48

Kleinbock, Dmitry, and Barak Weiss. "Modified Schmidt games and a conjecture of Margulis." Journal of Modern Dynamics 7, no. 3 (2013): 429–60. http://dx.doi.org/10.3934/jmd.2013.7.429.

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49

Chicone, C. "Lyapunov-Schmidt Reduction and Melnikov Integrals for Bifurcation of Periodic Solutions in Coupled Oscillators." Journal of Differential Equations 112, no. 2 (September 1994): 407–47. http://dx.doi.org/10.1006/jdeq.1994.1110.

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50

Giraud, Luc, Serge Gratton, and Julien Langou. "A Rank-k Update Procedure for Reorthogonalizing the Orthogonal Factor from Modified Gram--Schmidt." SIAM Journal on Matrix Analysis and Applications 25, no. 4 (January 2004): 1163–77. http://dx.doi.org/10.1137/s0895479803424347.

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