Annotated Bibliography on Generalized Inverses and Applications

Well, Mr. Jacobi, here it is: all the generalized inversion of two generations of invertors who, knowingly or unknowingly, subscribed to (and extended) your dictum. Please forgive us if we have over-inverted, or if we have not always inverted in the natural and sensible way. (Some of us have inverted with labor and pain by using hints from a dean or a tenure and promotion committee that “you better invert more, or else you would be inverted.”)

[1]  J. Chipman,et al.  Projections, generalized inverses, and quadratic forms , 1964 .

[2]  R. E. Kalman,et al.  Controllability of linear dynamical systems , 1963 .

[3]  J. Koliha.  Pseudo-inverses of operators , 1974 .

[4]  R. Tewarson,et al.  Some comments on the solution of linear equations , 1969 .

[5]  Arthur S. Goldberger,et al.  Stepwise Least Squares: Residual Analysis and Specification Error , 1961 .

[6]  R. Duffin.  Some problems of mathematics and science , 1974 .

[7]  M. Z. Nashed,et al.  Steepest Descent for Singular Linear Operator Equations , 1970 .

[8]  A generalized Lax-Milgram theorem , 1968 .

[9]  An equational approach to products of relatively regular operators , 1976 .

[10]  J. Chipman.  Estimation and Aggregation in Econometrics: An Application of the Theory of Generalized Inverses , 1976 .

[11]  G. Golub,et al.  Numerical computations for univariate linear models , 1973 .

[12]  Terence Butler,et al.  On a Method of Courant for Minimizing Functionals , 1962 .

[13]  J. Hunter.  On the moments of Markov renewal processes , 1969, Advances in Applied Probability.

[14]  J. B. McGuire,et al.  Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters , 1962 .

[15]  R. Tewarson,et al.  ON SOLVING ILL‐CONDITIONED SYSTEMS OF LINEAR EQUATIONS* , 1972 .

[16]  On existence criteria and approximation procedures for integral equations of the first kind , 1975 .

[17]  R. Meyer.  Theoretical and Computational Aspects of Nonlinear Regression , 1970 .

[18]  R. Bouldin.  The Pseudo-Inverse of a Product , 1973 .

[19]  C. M. Shetty,et al.  Nonlinear programming without differentiability in banach spaces: necessary and sufficient constraint qualification , 1976 .

[20]  D. Carlson,et al.  Matrix Decompositions Involving the Schur Complement , 1975 .

[21]  W. W. Elliott.  Generalized Green's Functions for Compatible Differential Systems , 1928 .

[22]  J. Neuberger.  The lack of self-adjointness in three-point boundary value problems , 1966 .

[23]  P. D Robers,et al.  An interval programming algorithm for discrete linear L1 approximation problems , 1969 .

[24]  T. Helvig,et al.  Applications of the Pseudoinverse to Modeling , 1966 .

[25]  Calyampudi R. Rao.  A note on the IPM method in the Unified Theory of Linear Estimation , 1972 .

[26]  J. Ogawa.  On the independence of bilinear and quadratic forms of a random sample from a normal population , 1949 .

[27]  S. Hakimi,et al.  Analog methods for computation of the generalized inverse , 1968 .

[28]  N. Abdelmalek.  Round off error analysis for Gram-Schmidt method and solution of linear least squares problems , 1971 .

[29]  C. E. Langenhop,et al.  On Generalized Inverses of Matrices , 1967 .

[30]  R. Cottle.  Manifestations of the Schur complement , 1974 .

[31]  T. N. E. Greville,et al.  Solutions of the Matrix Equation $XAX = X$, and Relations between Oblique and Orthogonal Projectors , 1974 .

[32]  T. O. Lewis,et al.  Pseudoinverss of Postive Semidefeinite Matrices , 1968 .

[33]  David D. Morrison.  Remarks on the Unitary Triangularization of a Nonsymmetric Matrix , 1960, JACM.

[34]  R. E. Cline,et al.  Generalized inverses of certain Toeplitz matrices , 1974 .

[35]  An Extension of the Generalized Inverse of a Matrix , 1970 .

[36]  C. D. Meyer,et al.  Continuity properties of the Drazin pseudoinverse , 1975 .

[37]  S. Mitra,et al.  Generalized inverses of partitioned matrices and recalculation of least squares estimates for data or model changes , 1971 .

[38]  Adi Ben-Israel,et al.  Extremal solutions of linear equations and generalized inversion between Hilbert spaces , 1972 .

[39]  W. Reid.  Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems , 1963 .

[40]  T. Greville,et al.  The Souriau-Frame algorithm and the Drazin pseudoinverse , 1973 .

[41]  A. Charnes,et al.  Structural sensitivity analysis in linear programming and an exact product form left inverse , 1968 .

[42]  G. Stewart.  Modifying pivot elements in Gaussian elimination , 1974 .

[43]  L. Duane Pyle,et al.  The Generalized Inverse in Linear Programming: An Intersection Projection Method , 1973 .

[44]  Nai–Kuan Tsao.  A Note on Implementing the Householder Transformation , 1975 .

[45]  On generalized inverses of matrices , 1966 .

[46]  R. Plemmons.  Regular nonnegative matrices , 1973 .

[47]  D. Tucker.  Boundary Value Problems for Linear Differential Systems , 1969 .

[48]  T. N. E. Greville,et al.  On Smoothing a Finite Table: A Matrix Approach , 1957 .

[49]  R. Croisot,et al.  Demi-groupes inversifs et demi-groupes réunions de demi-groupes simples , 1953 .

[50]  H. P. Decell.  A special form of a generalized inverse of an arbitrary complex matrix , 1965 .

[51]  On the compensation of multivariable control systems , 1968 .

[52]  The Eigenvalues and Singular Values of Matrix Sums and Products. VII (1) , 1973 .

[53]  W. G. Cochran,et al.  The distribution of quadratic forms in a normal system, with applications to the analysis of covariance , 1934, Mathematical Proceedings of the Cambridge Philosophical Society.

[54]  M. A. Kaashoek.  Stability Theorems for Closed Linear Operators , 1965 .

[55]  A. C. Aitken.  IV.—On Least Squares and Linear Combination of Observations , 1936 .

[56]  A linear differential system with general linear boundary conditions , 1969 .

[57]  Precompact linear operators in locally convex spaces , 1957 .

[58]  T. Whitney,et al.  Two Algorithms Related to the Method of Steepest Descent , 1967 .

[59]  William G. Wee,et al.  Generalized Inverse Approach to Adaptive Multiclass Pattern Classification , 1968, IEEE Transactions on Computers.

[60]  P. Stein.  Some general theorems on iterants , 1952 .

[61]  J. R. Wall.  Generalized inverses of stochastic matrices , 1975 .

[62]  M. Zuhair Nashed,et al.  Perturbations and Approximations for Generalized Inverses and Linear Operator Equations , 1976 .

[63]  S. Kaniel,et al.  Spectral theory for Fredholm operators , 1963 .

[64]  F. M. Speed.  An Application of the Generalized Inverse to the One-Way Classification , 1974 .

[65]  C. R. Henderson.  ESTIMATION OF VARIANCE AND COVARIANCE COMPONENTS , 1953 .

[66]  S. Caradus.  Perturbation theory for generalized Fredholm operators. , 1974 .

[67]  L. Autonne.  Sur les groupes linéaires, réels et orthogonaux , 1902 .

[68]  J. H. Wilkinson,et al.  Note on the iterative refinement of least squares solution , 1966 .

[69]  P. A. Cook.  Estimates for the inverse of a matrix , 1975 .

[70]  D. L. Powers,et al.  On under- and over-determined initial value problems , 1974 .

[71]  J. Locker.  An existence analysis for nonlinear equations in Hilbert space , 1967 .

[72]  K. Tanabe.  Characterization of linear stationary iterative processes for solving a singular system of linear equations , 1974 .

[73]  E. B. Leach,et al.  A note on inverse function theorems , 1961 .

[74]  H. E. Salzer,et al.  Improved formulas for complete and partial summation of certain series. , 1961 .

[75]  On Singularity and Lebesgue Type Decomposition for Operator-Valued Measures* , 1971 .

[76]  H. Chernoff.  Locally Optimal Designs for Estimating Parameters , 1953 .

[77]  M. K. Gavurin.  Ill-conditioned systems of linear algebraic equations , 1963 .

[78]  Y. Ho,et al.  A Class of Iterative Procedures for Linear Inequalities , 1966 .

[79]  The commuting inverses of a square matrix , 1966 .

[80]  Nabih N. Abdelmalek,et al.  On the discrete linear L1 approximation and L1 solutions of overdetermined linear equations , 1974 .

[81]  N. S. Urquhart.  The Nature of the Lack of Uniqueness of Generalized Inverse Matrices , 1969 .

[82]  David C. Lay,et al.  Spectral Properties of Generalized Inverses of Linear Operators , 1975 .

[83]  C. B. Shaw,et al.  Improvement of the resolution of an instrument by numerical solution of an integral equation , 1972 .

[84]  Roy H. Wampler.  A Report on the Accuracy of Some Widely Used Least Squares Computer Programs , 1970 .

[85]  A. T. Craig,et al.  Note on the Independence of Certain Quadratic Forms , 1943 .

[86]  George P.H. Styan,et al.  A note-on equicofactor matrices , 1967 .

[87]  R. Curtain.  A Survey of Infinite-Dimensional Filtering , 1975 .

[88]  M. Nashed,et al.  Steepest descent for singular linear operators with nonclosed range , 1971 .

[89]  É. Picard.  Sur un thÉorÈme gÉnÉral relatif aux Équations intÉgrales de premiÈre espÈce et sur quelques problÈmes de physique mathÉmatique , 1910 .

[90]  C. S. Ballantine.  Products of EP matrices , 1975 .

[91]  V. Ashkenazi.  Strength of a triangulation layout (ill-conditioning analysis) , 1965 .

[92]  D. Audley,et al.  III-posed and well-posed problems in systems identification , 1974 .

[93]  M. Hestenes.  Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. , 1951 .

[94]  Antony Jameson,et al.  Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix , 1968 .

[95]  B. Green.  THE ORTHOGONAL APPROXIMATION OF AN OBLIQUE STRUCTURE IN FACTOR ANALYSIS , 1952 .

[96]  G. Sebestyen,et al.  An Algorithm for Non-Parametric Pattern Recognition , 1966, IEEE Trans. Electron. Comput..

[97]  A. Sobczyk.  Projections in Minkowski and Banach spaces , 1941 .

[98]  Ward Cheney,et al.  Note on a Paper by Zuhovickii˘ Concerning the Tchebycheff Problem for Linear Equations , 1958 .

[99]  Adi Ben-Israel,et al.  On Iterative Computation of Generalized Inverses and Associated Projections , 1966 .

[100]  V. Kublanovskaya.  Evaluation of a generalized inverse matrix and projector , 1966 .

[101]  J. H. Wilkinson,et al.  Solution of real and complex systems of linear equations , 1966 .

[102]  C. L. Budde,et al.  On the computation of a generalized inverse of a matrix , 1969 .

[103]  Sanjo Zlobec,et al.  An Explicit Form of the Moore–Penrose Inverse of an Arbitrary Complex Matrix , 1970 .

[104]  W. Burmeister.  Inversionsfreie Verfahren zur Lösung nichtlinearer Operatorgleichungen , 1972 .

[105]  V. V. Voevodin.  The method of regularization , 1969 .

[106]  P. Robert,et al.  On the group-inverse of a linear transformation , 1968 .

[107]  R. C. Thompson.  Principal submatrices IX: Interlacing inequalities for singular values of submatrices , 1972 .

[108]  Herbert S. Wilf,et al.  MATRIX INVERSION BY THE ANNIHILATION OF RANK , 1959 .

[109]  D. Westreich.  Banach space bifurcation theory , 1972 .

[110]  C. D. Meyer,et al.  EP Operators and Generalized Inverses , 1975, Canadian Mathematical Bulletin.

[111]  M. Nashed,et al.  A unified approach to generalized inverses of linear operators: II. Extremal and proximal properties , 1974 .

[112]  Generalized Least Squares Estimators for Randomized Fractional Replication Designs , 1964 .

[113]  George Marsaglia,et al.  Idempotent Matrices and Quadratic Forms in the General Linear Hypothesis , 1957 .

[114]  C. Langenhop.  On the Index of a Square Matrix , 1971 .

[115]  Adi Ben-Israel,et al.  An iterative method for computing the generalized inverse of an arbitrary matrix , 1965 .

[116]  R. Fletcher,et al.  A Class of Methods for Nonlinear Programming II Computational Experience , 1970 .

[117]  Donald H. Thomas,et al.  On Least-Squares Fitting of Two-Dimensional Data with a Special Structure , 1968 .

[118]  John S. Chipman,et al.  On Least Squares with Insufficient Observations , 1964 .

[119]  J. Boot,et al.  The Computation of the Generalized Inverse of singular or Rectangular Matrices , 1963 .

[120]  Einar Andersen.  Solution of great systems of normal equations together with an investigation of Andrae's dot-figure, an arithmetical-technical investigation , 1947 .

[121]  F. L. Bauer.  Optimally scaled matrices , 1963 .

[122]  Claudio Cohen.  An Investigation of the Geometry of Subspaces for Some Multivariate Statistical Models , 1969 .

[123]  R. Fletcher,et al.  A Technique for Orthogonalization , 1969 .

[124]  E. Beltrami.  A constructive proof of the Kuhn-Tucker multiplier rule , 1969 .

[125]  J. Locker.  Self-adjointness for multi-point differential operators , 1973 .

[126]  W. Schempp.  Iterative solution of linear operator equations in Hilbert space and optimal Euler methods , 1970 .

[127]  P. Bergmann,et al.  The Hamiltonian of the General Theory of Relativity with Electromagnetic Field , 1950 .

[128]  M. Bartlett.  An Inverse Matrix Adjustment Arising in Discriminant Analysis , 1951 .

[129]  E. A. Sylvestre,et al.  Elimination of Linear Parameters in Nonlinear Regression , 1971 .

[130]  R. Bellman.  A note on the summability of formal solutions of linear integral equations , 1950 .

[131]  T. L. Boullion,et al.  Computation of Pseudoinverse Matrices Using Residue Arithmetic , 1972 .

[132]  S. Twomey.  The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements , 1965 .

[133]  S. Caradus.  Operators with finite ascent and descent , 1966 .

[134]  Ned Anderson.  A generalization of the method of averages for overdetermined linear systems , 1975 .

[135]  W. Dück.  Einzelschrittverfahren zur Matrizeninversion , 1964 .

[136]  Richard M.-M. Chen,et al.  New Matrix Inversion Algorithms Based on Exchange Method , 1973, IEEE Transactions on Computers.

[137]  Calyampudi R. Rao,et al.  Projections under seminorms and generalized Moore Penrose inverses , 1974 .

[138]  J. S. Bradley.  Adjoint quasi-differential operators of Euler type , 1966 .

[139]  R. Pringle,et al.  Expressions for Generalized Inverses of a Bordered Matrix with Application to the Theory of Constrained Linear Models , 1970 .

[140]  L. Crone.  The singular value decomposition of matrices and cheap numerical filtering of systems of linear equations , 1972 .

[141]  Multivariable control system synthesis utilizing the generalized inverse of a matrix , 1967 .

[142]  John R. Rice,et al.  Direct solution of partial difference equations by tensor product methods , 1964 .

[143]  G. Styan,et al.  Equalities and Inequalities for Ranks of Matrices , 1974 .

[144]  A. Halanay,et al.  A boundary value problem and its adjoint , 1968 .

[145]  S. Caradus.  Operators of Riesz type. , 1966 .

[146]  M. Hestenes.  A ternary algebra with applications to matrices and linear transformations , 1962 .

[147]  L. A. Gale.  A modified-equations method for the least-squares solution of condition equations , 1955 .

[148]  Abraham Charnes,et al.  Modular Design, Generalized Inverses, and Convex Programming , 1965 .

[149]  G. Golub,et al.  Numerical techniques in mathematical programming , 1970 .

[150]  P. M. Prenter.  A Collection Method for the Numerical Solution of Integral Equations , 1973 .

[151]  σ-Transformationen in lokalbeschränkten Vektorräumen , 1966 .

[152]  Jack K. Hale,et al.  Alternative problems for nonlinear functional equations , 1968 .

[153]  John von Neumann,et al.  Rings of operators , 1961 .

[154]  On the solution of normal equations , 1965 .

[155]  V. A. Sposito.  Technical Note - Solutions of a Special Class of Linear Programming Problems , 1973, Oper. Res..

[156]  S. Mitra.  Unified Least Squares Approach to Linear Estimation in a General Gauss–Markov Model , 1973 .

[157]  W. Petryshyn,et al.  On the inversion of matrices and linear operators , 1965 .

[158]  C. Radhakrishna Rao,et al.  Unified theory of linear estimation , 1971 .

[159]  J. Meyer.  Generalized Inversion of Modified Matrices , 1973 .

[160]  Carl D. Meyer,et al.  Note on the Computation of the Generalized Inverse of a Matrix , 1966 .

[161]  J. Franklin.  On Tikhonov’s method for ill-posed problems , 1974 .

[162]  John von Neumann,et al.  On Regular Rings. , 1936 .

[163]  On the Singularity of a Certain Bordered Matrix , 1967 .

[164]  R. Merris.  Two problems involving schur functions , 1975 .

[165]  R. Plemmons.  Generalized Inverses of Boolean Relation Matrices , 1971 .

[166]  H. H. Schaefer.  On the singularities of an analytic function with values in a Banach space , 1960 .

[167]  P. M. Prenter,et al.  On the branching of solutions of quadratic differential equations , 1974 .

[168]  Algebraic and Diagonable Rings , 1956, Canadian Journal of Mathematics.

[169]  J. Meyer,et al.  Generalized Inverses of Triangular Matrices , 1970 .

[170]  Zusammenziehbarkeit der allgemeinen linearen Gruppe des Raumes c0 der Nullfolgen , 1966 .

[171]  On the state of a linear operator and its adjoint , 1960 .

[172]  W. Root.  On the structure of a class of system identification problems , 1971 .

[173]  G. Forsythe.  Pitfalls in computation, or why a math book isn''t enough , 1970 .

[174]  T. Helvig,et al.  Marginal and conditional distributions of singular distributions , 1965 .

[175]  G. Sharpe,et al.  On the Solution of Networks by Means of the Equicofactor Matrix , 1960 .

[176]  Pseudo-Inverses in the Analysis of Variance , 1964 .

[177]  Adi Ben-Israel,et al.  On the Geometry of Subspaces in Euclidean n-Spaces , 1967 .

[178]  G. S. Watson.  Prediction and the efficiency of least squares , 1972 .

[179]  G. Salinetti.  The generalized inverse in parametric programming , 1974 .

[180]  A. Meir,et al.  Minimum Moduli of Ordinary Differential Operators , 1971 .

[181]  F. M. Larkin.  Estimation of a non-negative function , 1969 .

[182]  H. Y. Huang.  A direct method for the general solution of a system of linear equations , 1975 .

[183]  A. Sluis.  Condition numbers and equilibration of matrices , 1969 .

[184]  J. Stearn.  Iterative solutions of normal equations , 1951 .

[185]  F. Gilfeather.  ASYMPTOTIC CONVERGENCE OF OPERATORS IN HILBERT SPACE , 1969 .

[186]  A. Ben-Israel,et al.  On the Explicit Solution of a Special Class of Linear Economic Models , 1970, Oper. Res..

[187]  J. H. Wilkinson,et al.  Iterative refinement of the solution of a positive definite system of equations , 1966 .

[188]  R. Tewarson.  A Direct Method for Generalized Matrix Inversion , 1967 .

[189]  H. Drygas.  The estimation of residual variance in regression analysis , 1972 .

[190]  W. Johnson.  ON QUASI-COMPLEMENTS , 1973 .

[191]  T. O. Lewis,et al.  Weak Spectral Inverses , 1972 .

[192]  B. Nagy.  On the stability of the index of unbounded linear transformations , 1952 .

[193]  V. E. Price,et al.  The latent roots and vectors of a singular matrix , 1964, Comput. J..

[194]  Abraham Charnes,et al.  An Explicit Solution of a Special Class of Linear Programming Problems , 1968, Oper. Res..

[195]  J. Varah,et al.  Computing Invariant Subspaces of a General Matrix when the Eigensystem is Poorly Conditioned , 1970 .

[196]  J. A. Clarkson.  Uniformly convex spaces , 1936 .

[197]  D. W. Robinson.  On the Generalized Inverse of an Arbitrary Linear Transformation , 1962 .

[198]  On the use of some extraneous information in the estimation of the coefficients of regression , 1964 .

[199]  Some Properties of the Souriau–Frame Algorithm with Application to the Inversion of Rational Matrices , 1975 .

[200]  Reginald P. Tewarson,et al.  Projection Methods for Solving Sparse Linear Systems , 1969, Comput. J..

[201]  Mapping properties of relatively regular operators , 1975 .

[202]  C. Lawson,et al.  Extensions and applications of the Householder algorithm for solving linear least squares problems , 1969 .

[203]  A. Charnes,et al.  On the Intersections of Cones and Subspaces , 1968 .

[204]  R. Raphael.  Some Remarks on Regular and Strongly Regular Rings , 1975, Canadian Mathematical Bulletin.

[205]  G. Golub.  Least squares, singular values and matrix approximations , 1968 .

[206]  The Pseudoinverse of a Composite Matrix of Circulants , 1973 .

[207]  O. Taussky.  Matrices C with Cn → 0 , 1964 .

[208]  W. A. Hurwitz.  On the pseudo-resolvent to the kernel of an integral equation , 1912 .

[209]  T. Greville.  Note on the Generalized Inverse of a Matrix Product , 1966 .

[210]  Methods of successive approximation for linear equations in Banach spaces , 1968 .

[211]  G. Zyskind,et al.  On Combinability of Information from Uncorrelated Linear Models by Simple Weighting , 1966 .

[212]  J. Riley.  Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix , 1955 .

[213]  K. Wong.  The eigenvalue problem λTx + Sx , 1974 .

[214]  $AX - XB = C$, Resultants and Generalized Inverses , 1975 .

[215]  Orthogonal transformations and improperly posed problems , 1973, Bulletin of the Australian Mathematical Society.

[216]  E. Hölder.  Die Lichtensteinsche Methode für die Entwicklung der zweiten Variation, angewandt auf das Problem von Lagrange , 1936 .

[217]  R. Tewarson.  An iterative method for computing generalized inverses , 1972 .

[218]  V. P. Sreedharan,et al.  Chebyshev and $l^1 $-Solutions of Linear Equations Using Least Squares Solutions , 1968 .

[219]  E. Stiefel.  Note on Jordan elimination, linear programming and Tchebycheff approximation , 1960 .

[220]  SUR LA RÉSOLUTION DE PROBLÈMES «INVERSES» EN HYDROGÉOLOGIE , 1970 .

[221]  S. Twomey,et al.  On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature , 1963, JACM.

[222]  P. Wedin.  Perturbation bounds in connection with singular value decomposition , 1972 .

[223]  Charles W. Groetsch,et al.  Representations of the generalized inverse , 1975 .

[224]  H. Keller,et al.  Iterations, perturbations and multiplicities for nonlinear bifurcation problems , 1972 .

[225]  King-Sun Fu,et al.  Selection and Ordering of Feature Observations in a Pattern Recognition System , 1968, Inf. Control..

[226]  J. Ben Rosen.  Chebyshev Solution of Large Linear Systems , 1967, J. Comput. Syst. Sci..

[227]  M. Lynn,et al.  The Use of Multiple Deflations in the Numerical Solution of Singular Systems of Equations, with Applications to Potential Theory , 1968 .

[228]  Adi Ben-Israel,et al.  A Hyperpower Iterative Method for Computing Matrix Products Involving the Generalized Inverse , 1971 .

[229]  A. Charnes,et al.  Contributions to the Theory of Generalized Inverses , 1963 .

[230]  Das verallgemeinerte Inverse einer Matrix über einem beliebigen Körper - analytisch betrachtet. , 1970 .

[231]  Valentin F. Turchin,et al.  The use of mathematical-statistics methods in the solution of incorrectly posed problems , 1971 .

[232]  Edward K. Blum,et al.  Solution of Eigenvalue Problems in Hilbert Spaces by a Gradient Method , 1974, J. Comput. Syst. Sci..

[233]  L. Mirsky.  SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS , 1960 .

[234]  Solution of certain matrix equations , 1972 .

[235]  J. Meyer,et al.  Generalized Inverses and Ranks of Block Matrices , 1973 .

[236]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[237]  R. Rado,et al.  Note on generalized inverses of matrices , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[238]  An initial value method for solving Fredholm integral equation of the first kind , 1974 .

[239]  R. Bouldin.  The numerical range of a product , 1970 .

[240]  J. P. Williams,et al.  Extensions of the minimum effort control problem , 1966 .

[241]  Adi Ben-Israel,et al.  On Generalized Matrix Functions , 1973 .

[242]  G. Poole,et al.  Weak Spectral Inverses which are Partial Isometries , 1972 .

[243]  P. Odell,et al.  An Alternate Definition of a Pseudoinverse of a Matrix , 1966 .

[244]  Y. K. Kwon,et al.  Remarks on linear equations in banach space , 1969 .

[245]  J. Rice.  Experiments on Gram-Schmidt orthogonalization , 1966 .

[246]  G. Wahba,et al.  Regularization and approximation of linear operator equations in reproducing kernel spaces , 1974 .

[247]  G. Poole.  Generalized $M$-matrices and applications , 1975 .

[248]  D. Boggs.  A Partial-Step Algorithm for the Nonlinear Estimation Problem , 1972 .

[249]  W. V. Petryshyn.  On projectional-solvability and the Fredholm alternative for equations involving linear A-proper operators , 1968 .

[250]  W. Hemmerle.  An Explicit Solution for Generalized Ridge Regression , 1975 .

[251]  C. E. Rickart.  Banach Algebras With an Adjoint Operation , 1946 .

[252]  M. Fisher,et al.  Asymptotic behavior of Toeplitz matrices and determinants , 1969 .

[253]  Sujit Kumar Mitra,et al.  Fixed rank solutions of linear matrix equations , 1972 .

[254]  V. Williams.  Closed Fredholm and semi-Fredholm operators, essential spectra and perturbations , 1975 .

[255]  Calyampudi R. Rao,et al.  Some results in estimation and tests of linear hypotheses under the gauss-markoff model , 1968 .

[256]  K. Tanabe.  Neumann-type expansion of reflexive generalized inverses of a matrix and the hyperpower iterative method , 1975 .

[257]  R. Penrose.  On best approximate solutions of linear matrix equations , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[258]  Å. Björck,et al.  An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix , 1971 .

[259]  Stephen F. McCormick,et al.  A General Approach to One-Step Iterative Methods with Application to Eigenvalue Problems , 1972, J. Comput. Syst. Sci..

[260]  David Q. Mayne.  On the calculation of pseudoinverses , 1969 .

[261]  OPERATORS WITH α -CLOSED RANGE , 1972 .

[262]  James Hardy Wilkinson,et al.  The Calculation of Eigenvectors by the Method of Lanczos , 1958, Comput. J..

[263]  James W. Longley.  An Appraisal of Least Squares Programs for the Electronic Computer from the Point of View of the User , 1967 .

[264]  J. Varah.  On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems , 1973 .

[265]  Charles Henry Burris.  The numerical solution of the generalized eigenvalue problem for rectangular matrices , 1974 .

[266]  C. Helstrom.  Image Restoration by the Method of Least Squares , 1967 .

[267]  L. Brand.  The Solution of Linear Algebraic Equations , 1962, The Mathematical Gazette.

[268]  The use of mathematical programming for solving singular and poorly conditioned systems of equations , 1967 .

[269]  Adi Ben-Israel,et al.  An Elimination Method for Computing the Generalized Inverse of an Arbitrary Complex Matrix , 1963, JACM.

[270]  W. Reid.  Principal solutions of nonoscillatory linear differential systems , 1964 .

[271]  O. Taussky,et al.  On the theory of orders, in particular on the semigroup of ideal classes and genera of an order in an algebraic number field , 1962 .

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