| [Abalenkovs_etal:2017] | Abalenkovs, M., Bagherpour, N., Dongarra, J., Gates, .M., Haidar, A., Kurzak, J., Luszczek, P., Relton, S., Sistek, J., Stevens, D., Wu, P., Yamazaki, I., Asim YarKhan, A., and Zounon, M., (2017a) PLASMA 17.1 Functionality Report LAPACK Working Notes 293 (lawn293 and UT-EECS-17-751 ). Available at: http://www.netlib.org/lapack/lawnspdf/lawn293.pdf |
| [Abramowitz_Stegun:1970] | Abramowitz, M., and Stegun, I.A., (1970) Handbook of Mathematical Functions. New York, Dover Publications. |
| [Anda_Park:1994] | Anda, A.A. and Park, H., (1994) Fast plane rotations with dynamic scaling. Siam J. Matrix Anal. Appl., 15, 162-174. DOI: https://doi.org/10.1137/S0895479890193017 |
| [Anderson_etal:1999] | Anderson, E., Bai, Z., Bischof, C., Blacford, S., Demmel, J., Dongarra, J., Croz, J.D., Greenbaum, A., Hammarling, S., McKenney, A., and Sorensen, D., (1999) LAPACK User’s Guide. 3rd Ed. SIAM, Philadelphia, PA. DOI: https://doi.org/10.1137/1.9780898719604 |
| [Anderson_Fahey:1997] | Anderson, E., and Fahey, M., (1997) Performance improvements to LAPACK for the Cray Scientific Library. LAPACK Working Note No 126. Available at: http://www.netlib.org/lapack/lawnspdf/lawn126.pdf |
| [Bailey:1990] | Bailey, D., (1990) FFTs in External or Hierarchical Memory. The Journal of Supercomputing, 4:1, 23-35. DOI: https://doi.org/10.1007/BF00162341 |
| [Barlow_etal:2005] | Barlow, J.L., Bosner, N., and Drmac, Z., (2005) A new stable bidiagonal reduction algorithm. Linear Algebra Appl., 397:1, 35-84. DOI: https://doi.org/10.1016/j.laa.2004.09.019 |
| [Barnard:1978] | Barnard, J., (1978) Algorithm AS126: Probability Integral of the normal range. Appl. Statist., 27:2, 197-198. DOI: https://doi.org/10.2307/2346956 |
| [Berry_etal:1990] | Berry, K.J., Mielke, P.W., and Cran, G.W., (1990) Algorithm AS R83: A remark on Algorithm AS 109: Inverse of the Incomplete Beta Function Ratio. Appl. Statist., 39:2, 309-310. DOI: https://doi.org/10.2307/2347779 |
| [Berry_etal:1991] | Berry, K.J., Mielke, P.W., and Cran, G.W., (1991) Correction to Algorithm AS R83: A remark on Algorithm AS 109: Inverse of the Incomplete Beta Function Ratio. Appl. Statist., 40:1, p.236. |
| [Best_Roberts:1975] | Best, D.J., and Roberts, D.E., (1975) Algorithm AS 91: The Percentage Points of the chi2 Distribution. Appl. Statist., 24:3, 385-388. DOI: https://doi.org/10.2307/2347113 |
| [Bini_etal:2005] | Bini, D.A., Gemignani, L., and Tisseur, F., (2005) The Ehrlich-Aberth method for the nonsymmetric tridiagonal eigenvalue problem. SIAM J. Matrix Anal. Appl., 27:1, 153-175. DOI: https://doi.org/10.1137/S0895479803429788 |
| [Bjornsson_Venegas:1997] | Bjornsson, H., and Venegas, S.A., (1997) A manual for EOF and SVD analyses of climate data. McGill University, CCGCR Report No. 97-1, Montreal, Quebec, 52 PP. See: https://www.jsg.utexas.edu/fu/files/EOFSVD.pdf |
| [blas1] | Lawson, C.L., Hanson, R.J., Kincaid, D.R., and Krogh, F.T., (1979) Algorithm 539: Basic linear algebraic subprograms for fortran usage. ACM Trans. Math. Software 5, 3, 324-325. DOI: http://dx.doi.org/10.1145/355841.355848 |
| [blas2] | Dongarra, J.J., Du Croz, J., Hammarling, S., and Hanson, R.J., (1988) Algorithm 656: An extended set of basic linear algebra subprograms: Model implementation and test programs. ACM Trans. Math. Software 14, 1, 18-32. DOI: http://dx.doi.org/10.1145/42288.42292 |
| [blas3] | Dongarra, J.J., Du Croz, J., Hammarling, S., and Duff, I., (1990) Algorithm 679: A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Software 16, 1, 18-28. DOI: http://dx.doi.org/10.1145/77626.77627 |
| [Bloomfield:1976] | Bloomfield, P., (1976) Fourier analysis of time series- An introduction. John Wiley and Sons, New York. ISBN: 978-0-471-65399-8 |
| [Bosner_Barlow:2007] | Bosner, N., and Barlow, J.L., (2007) Block and Parallel versions of one-sided bidiagonalization. SIAM J. Matrix Anal. Appl., 29:3, 927-953. DOI: https://doi.org/10.1137/050636723 |
| [Braun_Kulperger:1997] | Braun, W.J., and Kulperger, R.J., (1997) Properties of a fourier bootstrap method for time series. Communications in Statistics - Theory and Methods, 26, 1329-1336. DOI: http://dx.doi.org/10.1080/03610929708831985 |
| [Bretherton_etal:1992] | Bretherton, C., Smith, c., and Wallace, J.M., (1992) An intercomparison of methods for finding coupled patterns in climate data. Journal of Climate, 5, 541-560. DOI: 10.1175/1520-0442(1992)005<0541:AIOMFF>2.0.CO;2 |
| [Buckley:1994a] | Buckley, A.G., (1994) Conversion to Fortran 90: a Case Study. ACM Transactions on Mathematical Software, 20(3), 308-353. DOI: http://dx.doi.org/10.1145/192115.192139 |
| [Buckley:1994b] | Buckley, A.G., (1994) Algorithm 734: A Fortran 90 Code for Unconstrained Nonlinear Minimization. ACM Transactions on Mathematical Software*, 20(3), 354-372. DOI: http://dx.doi.org/10.1145/192115.192146 |
| [Cleveland:1979] | Cleveland, W.S., (1979) Robust Locally Weighted Regression and Smoothing Scatterplots. Journal of the American Statistical Association, 74, 829-836. DOI: https://doi.org/10.1080/01621459.1979.10481038 |
| [Cleveland_Devlin:1988] | Cleveland, W.S., and Devlin, S.J., (1988) Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting. Journal of the American Statistical Association, 83, 596-610. DOI: https://doi.org/10.1080/01621459.1988.10478639 |
| [Cleveland_etal:1990] | Cleveland, R.B., Cleveland, W.S., McRae, J.E., and Terpennings, I., (1990) A Seasonal-Trend Decomposition Procedure Based on Loess. See http://www.jos.nu/Articles/abstract.asp?article=613 |
| [Coates_Diggle:1986] | Coates, D.S., and Diggle, P.J., (1986) Tests for comparing two estimated spectral densities. Journal of Time series Analysis, 7:1, 7-20. DOI: https://doi.org/10.1111/j.1467-9892.1986.tb00482.x |
| [Cody:1988] | Cody, W.J., (1988) Algorithm 665: MACHAR: A Subroutine to Dynamically Determine Machine Parameters. ACM Transactions on Mathematical Software, 14:4, 303-311. DOI: https://doi.org/10.1145/50063.51907 |
| [Cody_Coonen:1993] | Cody, W.J., and Coonen, J.T., (1993) Algorithm 722_ Functions to Support the IEEE Standard for Binary Floating-Point Arithmetic. ACM Transactions on Mathematical Software, 19:4, 443-451. DOI: https://doi.org/10.1145/168173.168185 |
| [Cooley_etal:1969] | Cooley, J.W., Lewis, P., and Welch, P., (1969) The Fast Fourier Transform and its Applications. IEEE Trans on Education, 12:1, 27-34. DOI: https://doi.org/10.1109/TE.1969.4320436 |
| [Cooley_etal:1970] | Cooley, J.W., Lewis, P., and Welch, P., (1970) The application of the Fast Fourier Transform algorithm to the estimation of spectra and cross-spectra. Journal of Sound and Vibration, 12:3, 339-352. DOI: https://doi.org/10.1016/0022-460X(70)90076-3 |
| [Cooper:1968] | Cooper, B.E., (1968) The integral of student’s t distribution (Algorithm AS3). Applied Statistics, 17:2, 189-190. DOI: https://doi.org/10.2307/2985684 |
| [Cran_etal:1977] | Cran, G.W., Martin, K.J., and Thomas, G.E., (1977) Remark AS R19 and Algorithm AS 109: A remark on Algorithms: AS 63 the Incomplete Beta integral, AS 64 Inverse of the Incomplete Beta Function Ratio. Appl. Statist., 26:1, 111-114. DOI: https://doi.org/10.2307/2346887 |
| [Davison_Hinkley:1997] | Davison, A.C., and Hinkley, D.V., (1997) Bootstrap methods and their application. Cambridge Univesity press, Cambridge, UK, 484 pp. DOI: https://doi.org/10.1017/CBO9780511802843 |
| [Demmel_Kahan:1990] | Demmel, J.W., and Kahan, W., (1990) Accurate singular values of bidiagonal matrices. SIAM Journal of Scientific and Statistical Computing, 11:5, 873-912. DOI: https://doi.org/10.1137/0911052 |
| [Demmel_etal:1993] | Demmel, J., Heath, M.T., and Van Der Vorst, H., (1993) Parallel numerical linear algebra. Acta Numerica, 2, 111-197. DOI: https://doi.org/10.1017/S096249290000235X |
| [Dhillon:1998] | Dhillon, I.S., (1998) Current inverse iteration software can fail. BIT, 38:4, 685-704. DOI: https://doi.org/10.1007/BF02510409 |
| [Diggle:1990] | Diggle, P.J., (1990) Time series: a biostatistical introduction. Clarendon Press, Oxford, 257 pp. ISBN-10: 0198522266 |
| [Diggle_Fisher:1991] | Diggle, P.J., and Fisher, N.I., (1991) Nonparametric comparison of cumulative periodograms. Applied Statistics, 40:3, 423-434. DOI: https://doi.org/10.2307/2347522 |
| [Dongarra_etal:1989] | Dongarra, J.J., Sorensen, D.C., and Hammarling, S.J., (1989) Block reduction of matrices to condensed form for eigenvalue computations. Journal of Computational and Applied Mathematics, 27:1-2, 215-227. DOI: |
| [Doornik:2007] | Doornik, J.A, (2007) Conversion of high-period random numbers to floating point. ACM Transactions on Modeling and Computer Simulation, 17:1, Article No. 3. DOI: https://doi.org/10.1145/1189756.1189759 |
| [Duchon:1979] | Duchon, C., (1979) Lanczos filtering in one and two dimensions. Journal of applied meteorology, 18:8, 1016-1022. DOI: 10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2 |
| [Ebisuzaki:1997] | Ebisuzaki, W., (1997) A method to estimate the statistical significance of a correlation when the data are serially correlated. Journal of climate, 10, 2147-2153. DOI: https://doi.org/10.1175/1520-0442%281997%29010%3C2147%3AAMTETS%3E2.0.CO%3B2 |
| [Erichson_etal:2019] | Erichson, N.B., Voronin, S., Brunton, S.L., and Kutz, J.N., (2019) Randomized matrix decompositions using R. arXiv.1608.02148. See https://arxiv.org/abs/1608.02148 |
| [Fernando:1997] | Fernando, K.V., (1997) On computing an eigenvector of a tridiagonal matrix. Part I: Basic results. Siam J. Matrix Anal. Appl., 18:4, 1013-1034. DOI: https://doi.org/10.1137/S0895479895294484 |
| [Fernando:1998] | Fernando, K.V., (1998) Accurately counting singular values of bidiagonal matrices and eigenvalues of skew-symmetric tridiagonal matrices. SIAM J. Matrix Anal. Appl., 20:2, 373-399. DOI: https://doi.org/10.1137/S089547989631175X |
| [Fortran] | Metcalf, M., Reid, J., and Cohen, M., (2013) Modern FORTRAN Explained. 7rd Ed., Oxford University Press, Oxford, UK. |
| [Gentleman_Marovich:1974] | Gentleman, W.M., and Marovich, S.B., (1974) More on algorithms that reveal properties of floating point arithmetic units. Communications of the ACM, 17:5, 276-277. DOI: https://doi.org/10.1145/360980.361003 |
| [Godunov_etal:1993] | S.K. Godunov, A.G. Antonov, O.P. Kiriljuk, V.I. Kostin (1993) Guaranteed Accuracy in Numerical Linear Algebra. Kluwer Academic. (A revised translation of a Russian text first published in 1988 in Novosibirsk) |
| [Goertzel:1958] | Goertzel, G., (1958) An Algorithm for the Evaluation of Finite Trigonometric Series. The American Mathematical Monthly, 65:1, 34-35. DOI: https://doi.org/10.2307/2310304 |
| [Goldstein:1973] | Goldstein, R.B., (1973) Chi-square quantiles. Comm. A.C.M., 16:8, 483-485. DOI: https://doi.org/10.1145/355609.362319 |
| [Golub_VanLoan:1996] | Golub, G.H., and Van Loan, C., (1996) Matrix Computations. 3rd Ed., The John Hopkins University Press, Baltimore, MD. |
| [Greenbaum_Dongarra:1989] | Greenbaum, A., and Dongarra, J., (1989) Experiments with QR/QL Methods for the Symmetric Tridiagonal Eigenproblem. LAPACK Working Note No 17. |
| [Gu:2015] | Gu, M., (2015) Subspace iteration randomization and singular value problems. SIAM J. Sci. Comput. Comm., 37, A1139-A1173. DOI: https://doi.org/10.1137/130938700 |
| [Hansen_etal:2012] | Hansen, P.C., Pereyra, V., and Scherer, G., (2012) Least Squares Data Fitting with Applications. Johns Hopkins University Press, 328 pp. ISBN:9781421407869 |
| [Halko_etal:2011] | Halko, N., Martinsson, P.G., Tropp, J.A., (2011) Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev., 53, 217-288. DOI: https://doi.org/10.1137/090771806 |
| [Harase:2014] | Harase, S., (2014) On the F2-linear relations of Mersenne Twister pseudorandom number generators. Mathematics and Computers in Simulation, 100, 103-113. DOI: https://doi.org/10.1016/j.matcom.2014.02.002 |
| [Hart:1978] | Hart, J.F., (1978) Computer Approximations. Krieger Publishing Co., Inc. Melbourne, FL, USA. ISBN:0882756427 |
| [Hegland_etal:1999] | Hegland, M., Kahn, M., and Osborn, M., (1999) A parallel algorithm for the reduction to tridiagonal form for eigendecomposition. SIAM Journal on Scientific Computing, 21:3, 987-1005. DOI: https://doi.org/10.1137/S1064827595296719 |
| [Hennecke:1995] | Hennecke, M., (1995) A Fortran90 interface to random number generation. Computer programs in physics, 90 (1), 117-120. DOI: https://doi.org/10.1016/0010-4655(95)00065-N |
| [Higham:2009] | Higham, N.J., (2009) Cholesky factorization. Wiley Interdisciplinary Reviews: Computational Statistics, 1, 251-254. DOI: https://doi.org/10.1002/wics.018 |
| [Higham:2011] | Higham, N.J., (2011) Gaussian elimination. Wiley Interdisciplinary Reviews: Computational Statistics, 3:3, 230-238. DOI: https://doi.org/10.1002/wics.164 |
| [Hill:1970] | Hill, G.W., (1970) Student’s t-distribution (Algorithm 395). Comm. A.C.M., 13:10, 617-619. DOI: https://doi.org/10.1145/355598.355599 |
| [Hill:1970b] | Hill, G.W., (1970) Student’s t-quantiles (Algorithm 396). Comm. A.C.M., 13:10, 619-620. DOI: https://doi.org/10.1145/355598.355600 |
| [Hill:1973] | Hill, I.D., (1973) Algorithm AS66: The Normal Integral. Appl. Statist., 22:3, 424-427. DOI: https://doi.org/10.2307/2346800 |
| [Howell_etal:2008] | Howell, G.W., Demmel, J., Fulton, C.T., Hammarling, S., and Marmol, K., (2008) Cache efficient bidiagonalization using BLAS 2.5 operators. ACM Transactions on Mathematical Software (TOMS), 34:3, Article 14. DOI: https://doi.org/10.1145/1356052.1356055 |
| [Iacobucci_Noullez:2005] | Iacobucci, A., and Noullez, A., (2005) A Frequency Selective Filter for Short-Length Time Series. Computational Economics, 25:1-2,75-102. DOI: https://doi.org/10.1007/s10614-005-6276-7 |
| [Ipsen:1997] | Ipsen, I.C.F., (1997) Computing an eigenvector with inverse iteration. SIAM Review, 39:2, 254-291. DOI: https://doi.org/10.1137/S0036144596300773 |
| [Jenkins_Watts:1968] | Jenkins, G.M., and Watts, D.G., (1968) Spectral Analysis and its Applications. San Francisco: Holden-Day. ISBN-10: 0816244642 |
| [Knuth:1997] | Knuth, D.E., (1997) The Art of Computer Programming, Volume III: Sorting and Searching. 3rd Ed, Addison-Wesley, Reading, MA, USA. ISBN 0201896850. |
| [Lanczos:1964] | Lanczos, C., (1964) A precision approximation of the gamma function. J. SIAM Numer. Anal., B, 1:1, 86-96. DOI: https://doi.org/10.1137/0701008 |
| [Lau:1980] | Lau, C.L., (1980) Algorithm AS 147: A simple series for the Incomplete Gamma Integral. Appl. Statist., 29:1, 113-114. DOI: https://doi.org/10.2307/2346431 |
| [Lawson_Hanson:1974] | Lawson, C.L., and Hanson, R.J., (1974) Solving least square problems. Prentice-Hall. DOI: https://doi.org/10.1137/1.9781611971217 |
| [LEcuyer:1999] | L’Ecuyer, P., (1999) Tables of Maximally-Equidistributed Combined LFSR Generators. Mathematics of computations, 68:225, 261-269. DOI: https://doi.org/10.1090/S0025-5718-99-01039-X |
| [Li_etal:2017] | Li, H.,Linderman, G.C., Szlam, A., Stanton, K.P., Kluger, Y., and Tygert, M., (2017) Algorithm 971: An implementation of a randomized algorithm for principal component analysis. ACM Transactions on Mathematical Software (TOMS), 43:3, Article 28. DOI: https://doi.org/10.1145/3004053 |
| [Majumder_Bhattacharjee:1973] | Majumder, K.L., and Bhattacharjee, G.P., (1973) Algorithm AS 63: the Incomplete Beta Integral. Appl. Statist., 22:3, 409-411. DOI: https://doi.org/10.2307/2346797 |
| [Malcolm:1972] | Malcolm, M.A., (1972) Algorithms to reveal properties of floating-point arithmetic. Communications of the ACM, 15:11, 949-951. DOI: https://doi.org/10.1145/355606.361870 |
| [Malyshev:2000] | Malyshev, A.N., (2000) On deflation for symmetric tridiagonal matrices. Report 182 of the Department of Informatics, University of Bergen, Norway. See: https://www.ii.uib.no/~sasha/mypapers/report/ii182.ps.gz |
| [Marques_Vasconcelos:2017] | Marques, O., and Vasconcelos, P.B., (2017) Computing the Bidiagonal SVD Through an Associated Tridiagonal Eigenproblem. In: Dutra I., Camacho R., Barbosa J., Marques O. (eds) High Performance Computing for Computational Science - VECPAR 2016. VECPAR 2016. Lecture Notes in Computer Science, vol 10150. Springer, Cham. DOI: https://doi.org/10.1007/978-3-319-61982-8_8 |
| [Marsaglia:1999] | Marsaglia, G., (1999) Random number generators for Fortran. Posted to the computer-programming-forum. See: http://computer-programming-forum.com/49-fortran/b89977aa62f72ee8.htm |
| [Marsaglia:2005] | Marsaglia, G., (2005) Double precision RNGs. Posted to the electronic billboard to sci.math.num-analysis. See: http://sci.tech-archive.net/Archive/sci.math.num-analysis/2005-11/msg00352.html |
| [Marsaglia:2007] | Marsaglia, G., (2007) Fortran and C: United with a KISS. Posted to the Google comp.lang.forum. See: http://groups.google.co.uk/group/comp.lang.fortran/msg/6edb8ad6ec5421a5 |
| [Martinsson_Voronin:2016] | Martinsson, P.G., and Voronin, S., (2016) A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM J. Sci. Comput., 38:5, S485-S507. DOI: https://doi.org/10.1137/15M1026080 |
| [Martinsson:2019] | Martinsson, P.G., (2019) Randomized methods for matrix computations. arXiv.1607.01649. See https://arxiv.org/abs/1607.01649 |
| [Mastronardi_etal:2006] | Mastronardi, M., Van Barel, M., Van Camp, E., and Vandebril, R., (2006) On computing the eigenvectors of a class of structured matrices. Journal of Computational and Applied Mathematics, 189:1-2, 580-591. DOI: https://doi.org/10.1016/j.cam.2005.03.048 |
| [Matsumoto_Nishimura:1998] | Matsumoto, M., and Nishimura, T., (1998) Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Transactions on Modeling and Computer Simulation, 8:1, 3-30. DOI: https://doi.org/10.1145/272991.272995 |
| [Monro_Branch:1977] | Monro, D.M., and Branch, J.L., (1997) Algorithm AS 117: The Chirp discrete Fourier transform of general length. Appl. Statist., 26:3, 351-361. DOI: https://doi.org/10.2307/2346986 |
| [Musco_Musco:2015] | Musco, C., and Musco, C., (2015) Randomized block krylov methods for stronger and faster approximate singular value decomposition. In Proceedings of the 28th International Conference on Neural Information Processing Systems, NIPS 15, pages 1396-1404, Cambridge, MA, USA, 2015. MIT Press. |
| [Noreen:1989] | Noreen, E.W., (1989) Computer-intensive methods for testing hypotheses: an introduction. Wiley and Sons, New York, USA, ISBN:978-0-471-61136-3 |
| [Olagnon:1996] | Olagnon, M., (1996) Traitement de donnees numeriques avec Fortran 90. Masson, 264 pages, Chapter 11.1.2, ISBN 2-225-85259-6. (in French) |
| [Oppenheim_Schafer:1999] | Oppenheim, A.V., and Schafer, R.W., (1999) Discrete-Time Signal Processing. 2rd Edition. Prentice-Hall, Signal Processing Series, New Jersey. ISBN-10: 0131988425 |
| [Parlett_Dhillon:1997] | Parlett, B.N., and Dhillon, I.S., (1997) Fernando’s solution to Wilkinsin’s problem: An application of double factorization. Linear Algebra and its Applications, 267, 247-279. DOI: https://doi.org/10.1016/S0024-3795(97)80053-5 |
| [Parlett:1998] | Parlett, B.N., (1998) The Symmetric Eigenvalue Problem. Revised edition, SIAM, Philadelphia. DOI: https://doi.org/10.1137/1.9781611971163 |
| [Peizer_Pratt:1968] | Peizer, D.B., and Pratt, J.W., (1968) A normal approximation for Binomial, F, Beta, and other common, related tail probabilities, I. J.A.S.A., 63:324, 1457-1483. DOI: https://doi.org/10.2307/2285895 |
| [Potscher_Reschenhofer:1988] | Potscher, B.,M., and Reschenhofer, E., (1988) Discriminating between two spectral densities in case of replicated observations. Journal of Time series Analysis, 9:3, 221-224. DOI: https://doi.org/10.1111/j.1467-9892.1988.tb00466.x |
| [Potscher_Reschenhofer:1989] | Potscher, B.,M., and Reschenhofer, E., (1989) Distribution of the Coates-Diggle test statistic in case of replicated observations. Statistics, 20:3, 417-421. DOI: https://doi.org/10.1080/02331888908802190 |
| [Priestley:1981] | Priestley, M.B., (1981) Spectral Analysis and Time Series. London: Academic Press. ISBN-10: 0125649223 |
| [Ralha:2003] | Ralha, R.M.S., (2003) One-sided reduction to bidiagonal form. Linear Algebra Appl., 358:1-3, 219-238. DOI: https://doi.org/10.1016/S0024-3795(01)00569-9 |
| [Reinsch_Bauer:1968] | Reinsch, C., and Bauer, F.L., (1968) Rational QR transformation with Newton shift for symmetric tridiagonal matrices. Numerische Mathematik, 11, 264-272. DOI: https://doi.org/10.1007/978-3-662-39778-7_17 |
| [Sedgewick:1998] | Sedgewick, R., (1998) Algorithms in C - Parts 1-4: Fundamentals, Data Structures, Sorting, Searching. 3rd Ed, Addison-Wesley, Reading, MA, USA. ISBN 978-0-201-31452-6. |
| [Shea:1988] | Shea, B.L., (1988) Algorithm AS 239: Chi-squared and Incomplete Gamma Integral. Appl. Statist., 37:3, 466-473. DOI: https://doi.org/10.2307/2347328 |
| [Shea:1991] | Shea, B.L., (1991) Algorithm AS R85 : A remark on AS 91: The Percentage Points of the chi2 Distribution. Appl. Statist., 40:1, pp.233-235. DOI: https://doi.org/10.2307/2347937 |
| [Stewart:1980] | Stewart, G.W., (1980) The efficient generation of random orthogonal matrices with an application to condition estimators. SIAM J. Numer. Anal., 17:3, 403-409. DOI: https://doi.org/10.1137/0717034 |
| [Stewart:2007] | Stewart, G.W., (2007) Block Gram-Schmidt Orthogonalization. Report TR-4823, Department of Computer Science, College Park, University of Maryland. |
| [Terray_etal:2003] | Terray, P., Delecluse, P., Labattu, S., Terray, L., (2003) Sea Surface Temperature associations with the Late Indian Summer Monsoon. Climate Dynamics, 21:7-8, 593-618. DOI: https://doi.org/10.1007/s00382-003-0354-0 |
| [Theiler_etal:1992] | Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J.D. (1992) Testing for nonlinearity in time series: the method of surrogate data. Physica D, 8, 77-94. DOI: https://doi.org/10.1016/0167-2789(92)90102-s |
| [Thomas_etal:2007] | Thomas, D.B., Luk, W., Leong, P.H.W., and Villasenor, J.D., (2007) Gaussian random number generators. ACM Comput. Surv., 39:4, Article 11, 38 pages. DOI: https://doi.org/10.1145/1287620.1287622. See: http://doi.acm.org/10.1145/1287620.1287622 |
| [VanZee_etal:2011] | Van Zee, F.G., Van de Geijn, R., and Quintana-Orti, G., (2011) Restructuring the QR Algorithm for High-Performance Application of Givens Rotations. FLAME Working Note 60. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-11-36. |
| [vonStorch_Zwiers:2002] | von Storch, H., and Zwiers, F.W., (2002) Statistical Analysis in Climate Research. Cambridge University Press, Cambridge, UK, 484 pp., ISBN:9780521012300 |
| [Walck:2007] | Walck, C., (2007) Hand-book on statistical distributions for experimentalists. Stockholm University, Internal Report SUF-PFY/96-01. See http://staff.fysik.su.se/~walck/suf9601.pdf |
| [Walker:1988] | Walker, H.F., (1988) Implementation of the GMRES method using Householder transformations. Siam J. Sci. Stat. Comput., 9:1, 152-163. DOI: https://doi.org/10.1137/0909010 |
| [Welch:1967] | Welch, P.D., (1967) The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE trans. on audio and electroacoustics, AU-15:2, 70-73. DOI: https://doi.org10.1109/TAU.1967.1161901 |
| [Wichura:1988] | Wichura, M.J., (1988) Algorithm AS 241: The percentage points of the normal distribution. Appl. Statist., 37:3, 477-484. DOI: https://doi.org/10.2307/2347330 |
| [Wilson_Hilferty:1931] | Wilson, E.B., and Hilferty, M.M., (1931) The distribution of Chi-square. Proc. Natl. Acad. Sci., USA, 17:12, 684-688. DOI: https://doi.org/10.1073/pnas.17.12.684 |
| [YarKhan_etal:2016] | YarKhan A., Kurzak, J., Luszczek, P., and Dongarra, J., (2016) Porting the PLASMA numerical library to the OpenMP standard. International Journal of Parallel Programming, 45: 612. DOI: https://doi.org/10.1007/s10766-016-0441-6 |
| [Yu_etal:2018] | Yu, W., Gu, Y., and Li, Y., (2018) Efficient randomized algorithms for the fixed-precision low-rank matrix approximation. SIAM J. Mat. Ana. Appl., 39:3, 1339-1359. DOI: https://doi.org/10.1137/17M1141977 |