48 BIBLIOGRAPHY13 (1988), no. 1, 4–14; MR 90a:15009a] by P. Bhimasankaram,Math. Sci. 13 (1988), no. 2, 152, (see[206]).1588. W. C. Rheinboldt, A unified convergence theory fora class of iterative processes, SIAM J. Numer. Anal.5 (1968), 42–63.1589. O. M. Ribits ′ ka, A fractional-analytic method offinding Moore-Penrose <strong>and</strong> Drasin pseudo-inversematrices, Mat. Metodi Fiz.-Mekh. Polya 39 (1996),no. 2, 140–143.1590. J. Rice, Experiments on gram–schmidt orthogonalization,Math. Comput. 20 (1966), 325–328.1591. M. Q. Rieck, Totally isotropic subspaces, complementarysubspaces, <strong>and</strong> generalized inverses, LinearAlgebra <strong>and</strong> its <strong>Applications</strong> 251 (1997), 239–248, (extension of a result of [1472]).1592. , Maximal orthogonality <strong>and</strong> pseudoorthogonalitywith applications to generalized inverses,Linear Algebra <strong>and</strong> its <strong>Applications</strong> 315(2000), no. 1-3, 155–173.1593. K. S. Riedel, A Sherman-Morrison-Woodbury identityfor rank augmenting matrices with applicationto centering, SIAM J. Matrix Anal. Appl. 13(1992), no. 2, 659–662, (see [598]).1594. R. F. Rinehart, The equivalence of definitions of amatric function, Amer. Math. Monthly 62 (1955),395–414.1595. W. Rising, <strong>Applications</strong> of generalized inverses toMarkov chains, Adv. in Appl. Probab. 23 (1991),293–302.1596. P. D. Robers <strong>and</strong> A. Ben-Israel, An interval programmingalgorithm for discrete linear L 1 approximationproblems, J. Approximation <strong>Theory</strong> 2(1969), 323–336.1597. , A suboptimization method for interval linearprogramming: A new method for linear programming,Linear Algebra <strong>and</strong> its <strong>Applications</strong> 3(1970), 383–405.1598. P. Robert, On the group-inverse of a linear transformation,J. Math. Anal. Appl. 22 (1968), 658–669.1599. D. W. Robinson, A proof of the composite functiontheorem for matric functions, Amer. Math.Monthly 64 (1957), 34–35.1600. , On the genralized inverse of an arbitrarylinear transformation, Amer. Math. Monthly 69(1962), 412–416.1601. , Gauss <strong>and</strong> generalized inverses, HistoriaMathematica 7 (1980), 118–125.1602. , On the covariance of the Moore-Penroseinverse, Linear Algebra <strong>and</strong> its <strong>Applications</strong> 61(1984), 91–99.1603. , Covariance of Moore-Penrose inverseswith respect to an invertible matrix, Linear Algebra<strong>and</strong> its <strong>Applications</strong> 71 (1985), 275–281.1604. , Nullities of submatrices of the Moore-Penrose inverse, Linear Algebra <strong>and</strong> its <strong>Applications</strong>94 (1987), 127–132.1605. , The determinantal rank idempotents ofa matrix, Linear Algebra <strong>and</strong> its <strong>Applications</strong>237/238 (1996), 83–96.1606. , The image of the adjoint mapping, LinearAlgebra <strong>and</strong> its <strong>Applications</strong> 277 (1998), no. 1-3,143–148.1607. , Separation of subspaces by volume, Amer.Math. Monthly 105 (1998), no. 1, 22–27.1608. D. W. Robinson <strong>and</strong> R. Puystjens, EP morphisms,Linear Algebra <strong>and</strong> its <strong>Applications</strong> 64 (1985),157–174.1609. , <strong>Generalized</strong> inverses of morphisms withkernels, Linear Algebra <strong>and</strong> its <strong>Applications</strong> 96(1987), 65–85.1610. D. W. Robinson, R. Puystjens, <strong>and</strong> J. Van Geel,Categories of matrices with only obvious Moore-Penrose inverses, Linear Algebra <strong>and</strong> its <strong>Applications</strong>97 (1987), 93–102.1611. S. M. Robinson, A short proof of Cramer’s rule,Math. Mag. 43 (1977), 94–95, (Reprinted in SelectedPapers on Algebra (S. Montgomery et al, editors),Math. Assoc. of Amer., 1977, pp. 313–314).1612. S. Roch <strong>and</strong> B. Silbermann, Asymptotic Moore-Penrose invertibility of singular integral operators,Integral Equations Operator <strong>Theory</strong> 26 (1996),no. 1, 81–101.1613. , Index calculus for approximation methods<strong>and</strong> singular value decomposition, J. Math. Anal.Appl. 225 (1998), no. 2, 401–426.1614. , Continuity of generalized inverses in Banachalgebras, Studia Math. 136 (1999), no. 3, 197–227.1615. R. T. Rockafellar, Convex Analysis, Princeton UniversityPress, Princeton, 1970.1616. C. A. Rohde, Contributions to the theory, computation<strong>and</strong> application of generalized inverses, Ph.d.,University of North Carolina, Raleigh, N.C., May1964.1617. , <strong>Generalized</strong> inverses of partitioned matrices,J. Soc. Indust. Appl. Math. 13 (1965), 1033–1035.1618. , Some results on generalized inverses,SIAM Rev. 8 (1966), 201–205.1619. , Special applications of the theory of generalizedmatrix inversion to statistics, In Boullion<strong>and</strong> Odell [255], pp. 239–266.1620. C. A. Rohde <strong>and</strong> J. R. Harvey, Unified least squaresanalysis, J. Amer. Statist. Assoc. 60 (1965), 523–527.1621. O. A. Romanova <strong>and</strong> N. A. Sidorov, The role ofSchmidt’s lemma <strong>and</strong> pseudoinverse operators inthe theory of differential equations with degeneration,Analytic Methods in the <strong>Theory</strong> of EllipticEquations, “Nauka” Sibirsk. Otdel., Novosibirsk,1982, pp. 82–88.1622. N. J. Rose, A note on computing the Drazin inverse,Linear Algebra <strong>and</strong> its <strong>Applications</strong> 15(1976), no. 2, 95–98.
1623. , The Laurent expansion of a generalizedresolvent with some applications, SIAM J. Math.Anal. 9 (1978), no. 4, 751–758.1624. J. B. Rosen, The gradient projection methodfor nonlinear programming. Part I: Linear Constraints,J. Soc. Indust. Appl. Math. 8 (1960), 181–217.1625. , The gradient projection method for nonlinearprogramming. Part II: Nonlinear Constraints,J. Soc. Indust. Appl. Math. 9 (1961), 514–532.1626. , Minimum <strong>and</strong> basic solutions to singularlinear systems, J. Soc. Indust. Appl. Math. 12(1964), 156–162.1627. , Chebyshev solutions of large linear systems,J. Comput. Syst. Sci. 1 (1967), 29–43.1628. M. Rosenberg, Range decomposition <strong>and</strong> generalizedinverse of nonnegative Hermitian matrices,SIAM Rev. 11 (1969), 568–571.1629. P. C. Rosenbloom, The method of steepest descent,Numerical Analysis. Proceedings of the SixthSymposium in Applied Mathematics, McGraw–HillBook Co., New York, 1956, pp. 127–176.1630. U. G. Rothblum, A representation of the Drazininverse <strong>and</strong> characterizations of the index, SIAMJ. Appl. Math. 31 (1976), no. 4, 646–648.1631. , Resolvent expansions of matrices <strong>and</strong> applications,Linear Algebra <strong>and</strong> its <strong>Applications</strong> 38(1981), 33–49.1632. A. L. Rukhin, Pattern correlation matrices <strong>and</strong>their properties, Linear Algebra <strong>and</strong> its <strong>Applications</strong>327 (2001), no. 1-3, 105–114.1633. B. Rust, W. R. Burrus, <strong>and</strong> C. Schneeberger, Asimple algorithm for computing the generalized inverseof a matrix, Comm. ACM 9 (1966), 381–385,387.1634. R. A. Šafiev, Methods for the computation of apseudoinverse operator, Akad. Nauk Azerbaĭdžan.SSR Dokl. 34 (1978), no. 1, 6–9.1635. , On the stability of pseudoinversion, Izv.Akad. Nauk Azerbaĭdzhan. SSR Ser. Fiz.-Tekhn.Mat. Nauk 1 (1980), no. 3, 3–10.1636. , L-pseudoinversion, Akad. Nauk Azerbaĭdzhan.SSR Dokl. 37 (1981), no. 5, 8–12.1637. , Regular methods of calculation of L-pseudoinverse operators, Zh. Vychisl. Mat. i Mat.Fiz. 23 (1983), no. 3, 536–544, (English translation:U.S.S.R. Comput. Math. <strong>and</strong> Math. Phys. 23(1983), no. 3, 14–19).1638. R. A. Šafiev <strong>and</strong> A. È. Babaeva, Pseudoinversion ofselfadjoint operators in Banach spaces, Izv. Akad.Nauk Azerbaĭdzhan. SSR Ser. Fiz.-Tekhn. Mat.Nauk 3 (1982), no. 6, 3–7 (1983).1639. S. Saitoh, Positive definite Hermitian matrices <strong>and</strong>reproducing kernels, Linear Algebra <strong>and</strong> its <strong>Applications</strong>48 (1982), 119–130.1640. , One approach to some general integraltransforms <strong>and</strong> its applications, Integral Transform.Spec. Funct. 3 (1995), no. 1, 49–84.BIBLIOGRAPHY 491641. , Integral Transforms, Reproducing Kernels<strong>and</strong> their <strong>Applications</strong>, Longman, Harlow, 1997.1642. , Representations of inverse functions,Proc. Amer. Math. Soc. 125 (1997), no. 12, 3633–3639.1643. S. Sakallioğlu <strong>and</strong> F. Akdeniz, Computation ofthe Moore-Penrose inverse of a matrix using thefull rank factorization, Pure Appl. Math. Sci. 39(1994), no. 1-2, 79–84.1644. S. Sakallıoğlu <strong>and</strong> F. Akdeniz, <strong>Generalized</strong> inverseestimator <strong>and</strong> comparison with least squares estimator,Turkish J. Math. 22 (1998), no. 1, 77–84.1645. G. Sali<strong>net</strong>ti, The generalized inverse in parametricprogramming, Calcolo 11 (1974), 351–363 (1975).1646. A. Sard, Approximation based on nonscalar observations,J. Approximation <strong>Theory</strong> 8 (1973), 315–334, (see [721]).1647. W. Sautter, A posteriori-Fehlerabschätzungen fürdie Pseudoinverse und die Lösung minimalerLänge, Computing 14 (1975), no. 1-2, 37–44.1648. K. Scharnhorst, Angles in complex vector spaces,Acta Applic<strong>and</strong>ae Mathematicae 69 (2001), 95–103.1649. H. Scheffé, An inverse problem in correlation theory,Amer. Math. Monthly 49 (1942), 99–104.1650. , The Analysis of Variance, Wiley, NewYork, 1959.1651. J. -P. Schellhorn, <strong>Generalized</strong> inverses <strong>and</strong> generalizedconvexity, Statistical Data Analysis <strong>and</strong> Inference(Neuchâtel, 1989), North-Holl<strong>and</strong>, Amsterdam,1989, pp. 445–455.1652. E. Schmidt, Zur Theorie der linearen undnichlinearen Integralgleichungen, I. Entwicklungwillküricher Funktionen nach Systemenvorgeschriebener, Math. Ann. 63 (1907), 433–476,(see SVD history in [1765])).1653. , Zur Theorie der linearen und nichlinearenIntegralgleichungen, II. Auflösung der allgemeinenlinearen Integralgleichung, Math. Ann. 64 (1907),161–174.1654. I. J. Schoenberg, Interpolating splines as limits ofpolynomials, Linear Algebra <strong>and</strong> its <strong>Applications</strong>52/53 (1983), 617–628.1655. P. H. Schönemann, A generalized solution of theorthogonal Procrustes problem, Psychmoetrika 31(1966), 1–10.1656. P. Schönfeld <strong>and</strong> H. -J. Werner, A note on C. R.Rao’s wider definition BLUE in the general Gauss-Markov model, Sankhyā Ser. B 49 (1987), no. 1,1–8.1657. M. Schreiber, Differential Forms: A Heuristic Introduction,Springer-Verlag, New York, 1977.1658. R. S. Schreiber, Computing generalized inverses<strong>and</strong> eigenvalues of symmetric matrices using systolicarrays, Computing Methods in Applied Sciences<strong>and</strong> Engineering, VI (Versailles, 1983),North-Holl<strong>and</strong>, Amsterdam, 1984, pp. 285–295.
- Page 1: Generalized Inverses: Theory and Ap
- Page 4 and 5: 4 BIBLIOGRAPHY30. J. K. Amburgey, T
- Page 6 and 7: 6 BIBLIOGRAPHY102. R. B. Bapat and
- Page 8 and 9: 8 BIBLIOGRAPHYHypercube Multiproces
- Page 10 and 11: 10 BIBLIOGRAPHY243. , On certain pr
- Page 12 and 13: 12 BIBLIOGRAPHY308. , Linear system
- Page 14 and 15: 14 BIBLIOGRAPHY379. Yong-Lin Chen a
- Page 16 and 17: 16 BIBLIOGRAPHY451. D. L. Davis and
- Page 18 and 19: 18 BIBLIOGRAPHY520. , Gauss-Markov
- Page 20 and 21: 20 BIBLIOGRAPHY594. M. Ferrante and
- Page 22 and 23: 22 BIBLIOGRAPHY664. A. J. Goldman a
- Page 24 and 25: 24 BIBLIOGRAPHY735. R. Grone, C. R.
- Page 26 and 27: 26 BIBLIOGRAPHY(Proc. Conf., Oberwo
- Page 28 and 29: 28 BIBLIOGRAPHY884. M. R. Hestenes,
- Page 30 and 31: 30 BIBLIOGRAPHY953. N. Jacobson, An
- Page 32 and 33: 32 BIBLIOGRAPHYlinearized waveform
- Page 34 and 35: 34 BIBLIOGRAPHYSympos. Math. Statis
- Page 36 and 37: 36 BIBLIOGRAPHYinequalities, SIAM R
- Page 38 and 39: 38 BIBLIOGRAPHY1234. G. Marsaglia a
- Page 40 and 41: 40 BIBLIOGRAPHY1301. , Minors of th
- Page 42 and 43: 42 BIBLIOGRAPHY1372. , An alternati
- Page 44 and 45: 44 BIBLIOGRAPHY1444. W. Oktaba, Tes
- Page 46 and 47: 46 BIBLIOGRAPHY1517. S. Puntanen an
- Page 50 and 51: 50 BIBLIOGRAPHY1659. R. S. Schreibe
- Page 52 and 53: 52 BIBLIOGRAPHY1733. A. G. Spera, R
- Page 54 and 55: 54 BIBLIOGRAPHYlinéaires, C. R. Ac
- Page 56 and 57: 56 BIBLIOGRAPHY1876. , The explicit
- Page 58 and 59: 58 BIBLIOGRAPHY1944. Guorong Wang a
- Page 60 and 61: 60 BIBLIOGRAPHY2014. Yimin Wei and
- Page 62 and 63: 62 BIBLIOGRAPHY2085. Tsuneo Yoshika