Esmaeili, H.; Pirnia, A. An efficient quadratically convergent iterative method to find the Moore-Penrose inverse. (English) Zbl 1372.65114 Int. J. Comput. Math. 94, No. 6, 1079-1088 (2017). The authors propose a new method to compute the Moore-Penrose pseudoinverse of a matrix. Their method is a Schulz-type iteration and converges quadratically. Systematic experiments and comparisons with similar methods are also presented. Reviewer: Constantin Popa (Constanţa) Cited in 5 Documents MSC: 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65F50 Computational methods for sparse matrices 65F10 Iterative numerical methods for linear systems Keywords:Moore-Penrose inverse; iterative method; Schulz-type method; second-order convergence; matrix multiplication; numerical examples PDFBibTeX XMLCite \textit{H. Esmaeili} and \textit{A. Pirnia}, Int. J. Comput. Math. 94, No. 6, 1079--1088 (2017; Zbl 1372.65114) Full Text: DOI References: [1] DOI: 10.1137/0703035 · Zbl 0143.37402 · doi:10.1137/0703035 [2] Ben-Israel A., Generalized Inverses, 2. ed. (2003) · Zbl 1026.15004 [3] Burden R.L., Numerical Analysis, 9. ed. (2011) [4] DOI: 10.1016/j.amc.2011.05.066 · Zbl 1298.65068 · doi:10.1016/j.amc.2011.05.066 [5] Cichocki A., Neural Networks for Optimization and Signal Processing (1993) · Zbl 0824.68101 [6] Krishnamurthy E.V., Numerical Algorithms: Computations in Science and Engineering (1986) [7] DOI: 10.1016/j.amc.2009.10.038 · Zbl 1185.65057 · doi:10.1016/j.amc.2009.10.038 [8] DOI: 10.1016/j.amc.2011.05.036 · Zbl 1226.65024 · doi:10.1016/j.amc.2011.05.036 [9] DOI: 10.2298/FIL1203453M · Zbl 1289.94014 · doi:10.2298/FIL1203453M [10] DOI: 10.1016/j.amc.2006.05.108 · Zbl 1104.65309 · doi:10.1016/j.amc.2006.05.108 [11] DOI: 10.1007/978-1-4612-0129-8 · doi:10.1007/978-1-4612-0129-8 [12] Pan V.Y., Newton’s Iteration for Matrix Inversion, Advances and Extensions, Matrix Methods: Theory Algorithms and Applications (2010) · Zbl 1215.65063 [13] DOI: 10.1137/0912058 · Zbl 0733.65023 · doi:10.1137/0912058 [14] DOI: 10.1137/080731220 · Zbl 1402.92026 · doi:10.1137/080731220 [15] DOI: 10.1002/zamm.19330130111 · JFM 59.0535.04 · doi:10.1002/zamm.19330130111 [16] DOI: 10.1007/978-1-4471-0449-0 · doi:10.1007/978-1-4471-0449-0 [17] DOI: 10.1007/BF02832365 · Zbl 1142.15006 · doi:10.1007/BF02832365 [18] DOI: 10.1016/j.aml.2013.10.004 · Zbl 1311.65035 · doi:10.1016/j.aml.2013.10.004 [19] DOI: 10.1016/j.amc.2013.07.039 · Zbl 1329.65073 · doi:10.1016/j.amc.2013.07.039 [20] Soleymani F., Appl. Math. Comput. 47 pp 33– (2015) [21] DOI: 10.1007/s12190-013-0743-4 · Zbl 1305.65128 · doi:10.1007/s12190-013-0743-4 [22] DOI: 10.1016/j.amc.2013.08.086 · Zbl 1336.65048 · doi:10.1016/j.amc.2013.08.086 [23] DOI: 10.1016/j.laa.2012.08.004 · Zbl 1258.65035 · doi:10.1016/j.laa.2012.08.004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.