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Preface to the Classics Edition

Preface

Introduction / 1：

Analysis of the Least Squares Problem / 2：

Orthogonal Decomposition by Certain Elementary Orthogonal Transformations / 3：

Orthogonal Decomposition by Singular Value Decomposition / 4：

Perturbation Theorems for Singular Values / 5：

Bounds for the Condition Number of a Triangular Matrix / 6：

The Pseudoinverse / 7：

Perturbation Bounds for the Pseudoinverse / 8：

Perturbation Bounds for the Solution of Problem LS / 9：

Numerical Computations Using Elementary Orthogonal Transformations / 10：

Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem / 11：

Computation of the Covariance Matrix of the Solution Parameters / 12：

Computing the Solution for the Underdetermined Full Rank Problem / 13：

Computing the Solution for Problem LS with Possibly Deficient Pseudorank / 14：

Analysis of Computing Errors for Householder Transformations / 15：

Analysis of Computing Errors for the Problem LS / 16：

Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic / 17：

Computation of the Singular Value Decomposition and the Solution of Problem LS / 18：

Other Methods for Least Squares Problems / 19：

Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space / 20：

Linear Least Squares with Linear Equality Constraints by Direct Elimination / 21：

Linear Least Squares with Linear Equality Constraints by Weighting / 22：

Linear Least Squares with Linear Inequality Constraints / 23：

Modifying a QR Decomposition to Add or Remove Column Vectors / 24：

Practical Analysis of Least Squares Problems / 25：

Examples of Some Methods of Analyzing a Least Squares Problem / 26：

Modifying a QR Decomposition to Add or Remove Row Vectors with Application to Sequential Processing of Problems Having a Large or Banded Coefficient Matrix / 27：

Basic Linear Algebra Including Projections / Appendix A：

Proof of Global Quadratic Convergence of the QR Algorithm / Appendix B：

Description and Use of FORTRAN Codes for Solving Problem LS / Appendix C：

Developments from 1974 to 1995 / Appendix D：

Bibliography

Index

Preface to the Classics Edition

Preface

Introduction / 1：

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Introduction to algebraic graph theory / 1：

Linear Algebra in Graphic Thoery / Part I：

The spectrum of a graph / 2：

Regular graphs and line graphs / 3：

Cycles and cuts / 4：

Spanning trees and associated structures / 5：

The tree-number / 6：

Determinant expansions / 7：

Vertex-partitions and the spectrum / 8：

Colouring Problems / Part II：

The chromatic polynomial / 9：

Subgraph expansions / 10：

The multiplicative expansion / 11：

The induced subgraph expansion / 12：

The Tutte polynomial / 13：

Chromatic polynomials and spanning trees / 14：

Symmetry and Regularity / Part III：

Automorphisms of graphs / 15：

Vertex-transitive graphs / 16：

Symmetric graphs / 17：

Symmetric graphs of degree three / 18：

The covering graph construction / 19：

Distance-transitive graphs / 20：

Feasibility of intersection arrays / 21：

Imprimitivity / 22：

Minimal regular graphs with given girth / 23：

References

Index

Introduction to algebraic graph theory / 1：

Linear Algebra in Graphic Thoery / Part I：

The spectrum of a graph / 2：

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