Symbolic and Numerical Computation for Artificial Intelligence

Contributors. Preface. Introduction. Polynomial Continuation and its Relationship to the Symbolic Reduction of Polynomial Systems. Elimination Methods: an Introduction. On the Solutions of a Set of Polynomial Equations. Quantifier Elimation for Conjunction of Linear Constraints via a Convex Hull Algoritm. Elimation Theory and Computer Vision: Recognition and Positioning of Curved 3D Objects from Range, Intensity, or Contours. 2D and 3D Object Recognition and Posiitioning with Algebraic Invariants and Covariants. Applications of Invariant Theory in Computer Vision. Distance Metrics for Comparing Shapes in the Plane. A Mathematical Framework for Combinational/Structural analysis of Linear Dynamical Systems by Means of Matroids. Symbolic Methods for the Simulation of Planar Mechanical Systems in Design. Basic Requirements for the Automatic Generation of FORTRAN code. Symbolic and Parallel Adaptive Methods for Partial Differential Equations. An Interactive Symbolic-Numeric Interface to Paralles ELLPACK for Building General PDE Solvers. Symbolic / Numeric Techniques in Modeling and Simulation. Symbolic and Numeric Computation: the Example of IRENA. Author Index. Index.

[1]  D. Hilbert.  Über die Theorie der algebraischen Formen , 1890 .

[2]  D. Hilbert,et al.  Ueber die vollen Invariantensysteme , 1893 .

[3]  A. L. Dixon.  The Eliminant of Three Quantics in two Independent Variables , 1909 .

[4]  F. S. Macaulay,et al.  The Algebraic Theory of Modular Systems , 1972 .

[5]  A. Albert.  Modern Higher Algebra , 1937 .

[6]  H. Weyl.  The Classical Groups , 1939 .

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

[8]  R. J. Walker.  Algebraic curves , 1950 .

[9]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[10]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[11]  R. Kálmán.  Mathematical description of linear dynamical systems , 1963 .

[12]  G. Gurevich,et al.  Foundation of the Theory of Algebraic Invariants , 1965, The Mathematical Gazette.

[13]  G. Gurevich,et al.  Foundations of the theory of algebraic invariants , 1966 .

[14]  H. Rosenbrock,et al.  State-space and multivariable theory, , 1970 .

[15]  Keith A. Paton,et al.  Conic sections in chromosome analysis , 1969, Pattern Recognit..

[16]  J. Dieudonne,et al.  Invariant theory, old and new , 1971 .

[17]  J. Dieudonné,et al.  La théorie des invariants au XIXe siècle , 1971 .

[18]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[19]  R. Biggerstaff,et al.  Three Variations in Dental Arch Form Estimated by a Quadratic Equation , 1972, Journal of dental research.

[20]  R. Brockett.  Lie Algebras and Lie Groups in Control Theory , 1973 .

[21]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[22]  Kenneth J. Turner,et al.  Computer perception of curved objects using a television camera , 1974 .

[23]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[24]  Ching-tai Lin.  Structural controllability , 1974 .

[25]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[26]  Bruce G. Baumgart,et al.  Geometric modeling for computer vision. , 1974 .

[27]  Antonio Albano,et al.  Representation of Digitized Contours in Terms of Conic Arcs and Straight-Line Segments , 1974, Comput. Graph. Image Process..

[28]  M. Docarmo.  Differential geometry of curves and surfaces , 1976 .

[29]  Hans Rademacher,et al.  Lectures on Elementary Number Theory , 1977 .

[30]  Ramanathan Gnanadesikan,et al.  Methods for statistical data analysis of multivariate observations , 1977, A Wiley publication in applied statistics.

[31]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

[32]  D. Hilbert,et al.  Hilbert's invariant theory papers , 1978 .

[33]  C. B. García,et al.  An Approach to Homotopy and Degree Theory , 1979, Math. Oper. Res..

[34]  F. Bookstein.  Fitting conic sections to scattered data , 1979 .

[35]  J. Yorke,et al.  A homotopy method for locating all zeros of a system of polynomials , 1979 .

[36]  J. Fitch.  The application of symbolic algebra to physics — A case of creeping flow , 1979 .

[37]  Donald B. Gennery,et al.  Object Detection and Measurement Using Stereo Vision , 1979, IJCAI.

[38]  Edward W. Ng.  Symbolic-Numeric Interface: a review (in absentia) , 1979, EUROSAM.

[39]  L. Watson.  A globally convergent algorithm for computing fixed points of C2 maps , 1979 .

[40]  E. Allgower,et al.  Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations , 1980 .

[41]  Barr,et al.  Superquadrics and Angle-Preserving Transformations , 1981, IEEE Computer Graphics and Applications.

[42]  P. J. Burt,et al.  Fast Filter Transforms for Image Processing , 1981 .

[43]  Dana H. Ballard,et al.  Generalizing the Hough transform to detect arbitrary shapes , 1981, Pattern Recognit..

[44]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Parabolic Equations. Part 1 , 1981 .

[45]  Rodney A. Brooks,et al.  Symbolic Reasoning Among 3-D Models and 2-D Images , 1981, Artif. Intell..

[46]  Ernest L. Hall,et al.  Measuring Curved Surfaces for Robot Vision , 1982, Computer.

[47]  PAUL D. SAMPSON,et al.  Fitting conic sections to "very scattered" data: An iterative refinement of the bookstein algorithm , 1982, Comput. Graph. Image Process..

[48]  M. Iri,et al.  Applications of Matroid Theory , 1982, ISMP.

[49]  James T. Kajiya,et al.  Ray tracing parametric patches , 1982, SIGGRAPH.

[50]  J. Ortega,et al.  A multi-color SOR method for parallel computation , 1982, ICPP.

[51]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[52]  Gene H. Golub,et al.  Matrix computations , 1983 .

[53]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[54]  Olivier D. Faugeras,et al.  A 3-D Recognition and Positioning Algorithm Using Geometrical Matching Between Primitive Surfaces , 1983, IJCAI.

[55]  Robert C. Bolles,et al.  3DPO: A Three- Dimensional Part Orientation System , 1986, IJCAI.

[56]  Alexander P. Morgan,et al.  A Method for Computing All Solutions to Systems of Polynomials Equations , 1983, TOMS.

[57]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[58]  Kokichi Sugihara,et al.  An Algebraic Approach to Shape-from-Image Problems , 1984, Artif. Intell..

[59]  P. Brunovský,et al.  Solving systems of polynomial equations by bounded and real homotopy , 1984 .

[60]  S. Helgason.  Groups and geometric analysis , 1984 .

[61]  W. Grimson,et al.  Model-Based Recognition and Localization from Sparse Range or Tactile Data , 1984 .

[62]  Berthold K. P. Horn.  Extended Gaussian images , 1984, Proceedings of the IEEE.

[63]  John Kenneth Salisbury,et al.  Interpretation of contact geometries from force measurements , 1984, ICRA.

[65]  J J Koenderink,et al.  What Does the Occluding Contour Tell Us about Solid Shape? , 1984, Perception.

[66]  Ron Goldman,et al.  Implicit representation of parametric curves and surfaces , 1984, Comput. Vis. Graph. Image Process..

[67]  Michael Safonov.  Exact calculation of the multivariable structured-singular-value stability margin , 1984, The 23rd IEEE Conference on Decision and Control.

[68]  David B. Cooper,et al.  Bayesian Recognition of Local 3-D Shape by Approximating Image Intensity Functions with Quadric Polynomials , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[69]  John R. Rice,et al.  Solving elliptic problems using ELLPACK , 1985, Springer series in computational mathematics.

[70]  Barbara L. Gates.  Gentran: an automatic code generation facility for REDUCE , 1985, SIGS.

[71]  Beresford N. Parlett,et al.  Element Preconditioning Using Splitting Techniques , 1985 .

[72]  A. Morgan,et al.  Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation Methods , 1985 .

[73]  K. Murota.  Use of the concept of physical dimensions in the structural approach to systems analysis , 1985 .

[74]  Alexander P. Morgan,et al.  Performance of algorithms for calculating the equilibrium composition of a mixture of gases , 1985 .

[75]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[76]  K. Sugihara.  Machine interpretation of line drawings , 1986, MIT Press series in artificial intelligence.

[77]  M. Hebert,et al.  The Representation, Recognition, and Locating of 3-D Objects , 1986 .

[78]  David B. Cooper,et al.  On Optimally Combining Pieces of Information, with Application to Estimating 3-D Complex-Object Position from Range Data , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[79]  L. Watson.  Numerical linear algebra aspects of globally convergent homotopy methods , 1986 .

[80]  Joseph E. Flaherty,et al.  A moving-mesh finite element method with local refinement for parabolic partial differential equations , 1986 .

[81]  Stanly Steinberg,et al.  Using MACSYMA to Write FORTRAN Subroutines , 1986, J. Symb. Comput..

[82]  Alexander P. Morgan.  A homotopy for solving polynomial systems , 1986 .

[83]  John F. Canny,et al.  Collision Detection for Moving Polyhedra , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[84]  J. Flaherty,et al.  A two-dimensional mesh moving technique for time-dependent partial differential equations , 1986 .

[85]  Alex Pentland,et al.  Perceptual Organization and the Representation of Natural Form , 1986, Artif. Intell..

[86]  Barbara L. Gates.  A numerical code generation facility for REDUCE , 1986, SYMSAC '86.

[87]  Paul S. Wang,et al.  FINGER: A Symbolic System for Automatic Generation of Numerical Programs in Finite Element Analysis , 1986, J. Symb. Comput..

[88]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[89]  A. Morgan,et al.  A methodology for solving chemical equilibrium systems , 1987 .

[90]  W. Eric L. Grimson,et al.  Localizing Overlapping Parts by Searching the Interpretation Tree , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[91]  K. Murota.  Refined study on structural controllability of descriptor systems by means of matroids , 1987 .

[92]  D. W. Thompson,et al.  Three-dimensional model matching from an unconstrained viewpoint , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[93]  K. R. Grice,et al.  Robust, geometrically based, automatic two‐dimensional mesh generation , 1987 .

[94]  R. Farouki.  Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations , 1987 .

[95]  Layne T. Watson,et al.  Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms , 1987, TOMS.

[96]  Vaughan R. Pratt,et al.  Direct least-squares fitting of algebraic surfaces , 1987, SIGGRAPH.

[97]  Jan J. Koenderink,et al.  An internal representation for solid shape based on the topological properties of the apparent contour , 1987 .

[98]  Radu Horaud,et al.  New Methods for Matching 3-D Objects with Single Perspective Views , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[99]  R. Bajcsy,et al.  Three dimensional object representation revisited , 1987 .

[100]  Kazuo Murota,et al.  Combinatorial canonical form of layered mixed matrices and its application to block-triangularization of systems of linear/nonlinear equations , 1987 .

[101]  Kristhan T. Gunnarsson,et al.  CAD Model-Based Localization of Parts in Manufacturing , 1987, Computer.

[102]  Bruno Buchberger,et al.  Applications of Gröbner Bases in Non-linear Computational Geometry , 1987, Trends in Computer Algebra.

[103]  Bruce Randall Donald,et al.  A Search Algorithm for Motion Planning with Six Degrees of Freedom , 1987, Artif. Intell..

[104]  A. Morgan.  Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems , 1987 .

[105]  R. Bajcsy,et al.  Shape recovery and segmentation with deformable part models , 1987 .

[106]  Yehezkel Lamdan,et al.  Object recognition by affine invariant matching , 2011, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[107]  Gabriel Taubin,et al.  Nonplanar curve and surface estimation in 3-space , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[108]  John E. Hopcroft,et al.  Towards implementing robust geometric computations , 1988, SCG '88.

[109]  Haim J. Wolfson,et al.  An improved model-based matching method using footprints , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[110]  Paul S. Wang.  An Introduction to Berkeley Unix , 1988 .

[111]  Ramesh C. Jain,et al.  Segmentation through Variable-Order Surface Fitting , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[112]  Isaac Weiss,et al.  Projective invariants of shapes , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[113]  J. Ortega.  Introduction to Parallel and Vector Solution of Linear Systems , 1988, Frontiers of Computer Science.

[114]  Ramesh C. Jain,et al.  Polynomial Methods For Structure From Motion , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[115]  Takeo Kanade,et al.  Automatic generation of object recognition programs , 1988, Proc. IEEE.

[116]  James A. Yorke,et al.  Numerically determining solutions of systems of polynomial equations , 1988 .

[117]  Yehezkel Lamdan,et al.  Geometric Hashing: A General And Efficient Model-based Recognition Scheme , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[118]  Terrance E. Boult,et al.  Error Of Fit Measures For Recovering Parametric Solids , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[119]  Ramakant Nevatia,et al.  Matching 3-D objects using surface descriptions , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[120]  Ronen Basri,et al.  The Alignment Of Objects With Smooth Surfaces , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[121]  Bruce Randall Donald.  The complexity of planar compliant motion planning under uncertainty , 1988, SCG '88.

[122]  Lars Nielsen,et al.  Automated guidance of vehicles using vision and projective invariant marking , 1988, Autom..

[123]  A. Recski.  Matroid theory and its applications in electric network theory and in statics , 1989 .

[124]  Ruud M. Bolle,et al.  Visual recognition using concurrent and layered parameter networks , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[125]  Chi-Wang Shu,et al.  TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework , 1989 .

[126]  Kazuo Murota,et al.  A matroid-theoretic approach to structurally fixed modes of control systems , 1989 .

[127]  W. Zulehner.  On the solutions to polynomial systems obtained by homotopy methods , 1989 .

[128]  Deepak Kapur,et al.  Geometric reasoning , 1989 .

[129]  Joseph E. Flaherty,et al.  Adaptive Methods for Partial Differential Equations , 1989 .

[130]  Kazuo Murota,et al.  On the irreducibility of layered mixed matrices , 1989 .

[131]  W. Eric L. Grimson.  On the Recognition of Curved Objects , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[132]  Bruce Randall Donald,et al.  On the Motion of Compliantly-Connected Rigid Bodies in Contact, Part 1: The Motion Prediction Problem , 1989 .

[133]  John R. Rice,et al.  Parallel (//) Ellpack PDE Solving System , 1989 .

[134]  J. Yorke,et al.  The cheater's homotopy: an efficient procedure for solving systems of polynomial equations , 1989 .

[135]  R. Jain,et al.  Generating aspect graphs for curved objects , 1989, [1989] Proceedings. Workshop on Interpretation of 3D Scenes.

[136]  D. Kriegman,et al.  On recognizing and positioning curved 3D objects from image contours , 1989, [1989] Proceedings. Workshop on Interpretation of 3D Scenes.

[137]  K. Murota.  Some recent results in combinatorial approaches to dynamical systems , 1989 .

[138]  Avinash C. Kak,et al.  A robot vision system for recognizing 3D objects in low-order polynomial time , 1989, IEEE Trans. Syst. Man Cybern..

[139]  Bruce Randall Donald,et al.  A provably good approximation algorithm for optimal-time trajectory planning , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[140]  Bruce Randall Donald,et al.  Error Detection and Recovery in Robotics , 1989, Lecture Notes in Computer Science.

[141]  Amy J. Briggs.  An efficient algorithm for one-step planar complaint motion planning with uncertainty , 1989, SCG '89.

[142]  David Shi Chen,et al.  A Data-Driven Intermediate Level Feature Extraction Algorithm , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[143]  John F. Canny,et al.  On computability of fine motion plans , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[144]  Alexander P. Morgan,et al.  Element variables and the solution of complex chemical equilibrium problems , 1989 .

[145]  Jean Ponce,et al.  Invariant Properties of Straight Homogeneous Generalized Cylinders and Their Contours , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[146]  Paul S. Wang,et al.  GENCRAY: a portable code generator for cray fortran , 1989, ISSAC '89.

[147]  Charles W. Wampler,et al.  Solving a Planar Four-Bar Design Problem Using Continuation , 1990 .

[148]  A. Morgan,et al.  Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics , 1990 .

[149]  M. Shephard,et al.  Parallel computation with adaptive methods for elliptic and hyperbolic systems , 1990 .

[150]  William Grimson,et al.  Object recognition by computer - the role of geometric constraints , 1991 .

[151]  David A. Forsyth,et al.  Projectively invariant representations using implicit algebraic curves , 1990, Image Vis. Comput..

[152]  Haim J. Wolfson.  On curve matching , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[153]  Zhenyu Li,et al.  Constructing strongly convex hulls using exact or rounded arithmetic , 1990, SCG '90.

[154]  Régis Vaillant.  Using Occluding Contours for 3D Object Modeling , 1990, ECCV.

[155]  John R. Rice,et al.  //ELLPACK: a numerical simulation programming environment for parallel MIMD machines , 1990, ICS '90.

[156]  Bruce Randall Donald,et al.  On the motion of compliantly-connected rigid bodies in contact. II. A system for analyzing designs for assembly , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[157]  Kevin W. Bowyer,et al.  Computing the orthographic projection aspect graph of solids of revolution , 1990, Pattern Recognit. Lett..

[158]  Kazuo Murota,et al.  Principal structure of layered mixed matrices , 1990, Discret. Appl. Math..

[159]  D. Kriegman,et al.  New progress in prediction and interpretation of line-drawings of curved 3D objects , 1990, Proceedings. 5th IEEE International Symposium on Intelligent Control 1990.

[160]  Peter K. Allen,et al.  Acquisition and interpretation of 3-D sensor data from touch , 1990, IEEE Trans. Robotics Autom..

[161]  M. G. Richardson,et al.  Reconciling Symbolic and Numeric Computation in a Practical Setting , 1990, DISCO.

[162]  David J. Kriegman,et al.  Object classes and image contours in model-based vision , 1990 .

[163]  A. Morgan,et al.  Computing singular solutions to nonlinear analytic systems , 1990 .

[164]  Joseph E. Flaherty,et al.  An adaptive mesh-moving and local refinement method for time-dependent partial differential equations , 1990, TOMS.

[165]  W. B. Seales,et al.  Constrained viewpoint from occluding contour , 1991, [1991 Proceedings] Workshop on Directions in Automated CAD-Based Vision.

[166]  Michael C. Dewar,et al.  Interfacing algebraic and numeric computation , 1991 .

[167]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[168]  Bernard Roth,et al.  Kinematic analysis of the 6R manipulator of general geometry , 1991 .

[169]  Satoru Fujishige,et al.  Submodular functions and optimization , 1991 .

[170]  Randy C. Brost,et al.  Graphical analysis of planar rigid-body dynamics with multiple frictional contacts , 1991 .

[171]  Kazuo Murota,et al.  On the Smith normal form of structured polynomial matrices , 1991 .

[172]  Victor J. Milenkovic,et al.  Numerical stability of algorithms for line arrangements , 1991, SCG '91.

[173]  K. Murota,et al.  Structure at infinity of structured descriptor systems and its applications , 1991 .

[174]  A. Morgan,et al.  SOLVING THE 6R INVERSE POSITION PROBLEM USING A GENERIC-CASE SOLUTION METHODOLOGY , 1991 .

[175]  Bruce Randall Donald,et al.  A rational rotation method for robust geometric algorithms , 1991, SCG '92.

[176]  Joseph E. Flaherty,et al.  Adaptive local overlapping grid methods for parabolic systems in two space dimensions , 1992 .

[177]  David J. Kriegman,et al.  On using CAD models to compute the pose of curved 3D objects , 1992, CVGIP Image Underst..

[178]  Rupak Biswas,et al.  An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws , 1993 .

[179]  Joseph E. Flaherty,et al.  A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems , 1993 .

[180]  Kazuo Murota,et al.  Mixed Matrices — Irreducibility and Decomposition — ⁄ , 1993 .

[181]  Kazuo Murota,et al.  Hierarchical decomposition of symmetric discrete systems by matroid and group theories , 1993, Math. Program..

[182]  N. Bose.  Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory , 1995 .

[183]  Robert D. Russell,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[184]  Randolph E. Bank,et al.  PLTMG - a software package for solving elliptic partial differential equations: users' guide 8.0 , 1998, Software, environments, tools.

[185]  W. Wells,et al.  Modern higher algebra , 2022 .