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| Moore R.E. — Methods and Applications of Interval Analysis |
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| Предметный указатель |
Absolute value of an interval 10
Adams, E. and Ames, W. F. 62 73 105 106 114 115
Adams, E. and Spreuer, H. 110 111 112 115
Ahmad, R. 17
Alefeld, G. 62 72
Alefeld, G. and Herzberger, J. 17 31 47 56 72
Ames, W. F. and Ginsberg 108 115
Analysis of a region 77
Apostolatos, N. and Kulisch, U. 17
Apostolatos, N., Kulisch, U., Krawczyk, R., Lortz, B., Nickel, K., and Wippemann, H. — W. 17
Appe’t W. 31 102 103 104 114
Avenhaus, J. 114
Bachmann, K. — H. 114
Beeck, H. 61 72
Bierbaum, F. 56
Bierbaum, F. and Schwierz, K. — P. 7
Bilateral algorithms 107—108
Bisection rules 78—81
Bisection search procedure 77
Cancellation law 14
Centered form 44—45
Chang, Y. F., Corliss, G., and Kriegsman, G. 99 115
Chemical reactor theory (application to) 71—72
Christ, H. 17
Chuba, W. and Miller, W. 72
Circular arithmetic in the complex plane 17
Coarsening see Degree reduction
Collatz, L. 106
Continuity of interval functions 33
Convex programming 88—90
Cyclic bisection 49 78 89—90
Daniel, J. W. and Moore, R. E. 114 115
Degenerate intervals 9
Degree reduction 30
Dempster 17
Derivative compatible enclosures 54 104
Diagonally dominant matrices 61
Differential equations 70—72 83—84 93—115
Differential inequalities 105—114
Dussel, R. 57 89 90 92
Dussel, R. and Schmitt, B. 50 57
Ecker, K. and Ratschek, H. 17
Ecosystems (application to) 98—99 113
Ellipsoids 17
Endpoints 9
Equal intervals 10
Excess width 35 42 44 45 47 48 50
Exclusion tests 76—77
Extended interval arithmetic 17 65 66—68
Finance (application to) 117—123
Finite convergence 36—38 51 53 56
Finite difference methods (applications to) 101 103 104 111—112
Fixed precision arithmetic 14
Forestry project (application to) 119—123
Fredholm integral equations 102
Functional analysis (applications to) 102
Gargantini, I. 17 73
Gargantini, I. and Henrici, P. 17 65 73
Glatz, G. 17
Global error bounds for initial value problems 93
Globally convergent interval Newton methods 65
Good, D. I. and London, R. L. 17
Gray, J. H. and Rail, L. B. 31 56 57
Greenspan, D. 99 115
Guderly, K. G. and Keller, C. L. 17
Gutterman, P. 7 123
Hansen, E. 44 56 62 65 72 73 92 101 114
Hansen, E. and Smith, R. 72
Harrison, G. W. 98 113 115
Hegben 72
Henrici, P. 6 17 31
Hunger, S. 114
Hussain, F. 7
Inclusion monotonicity 20—21 22 23 24 29 35 41 51 52 63 69—70
Initial value problems 93—99 106—110
Integral equations 69—72 93 100—101 107—110 112
Integration of interval functions 50—56
Internal rate of return 117—123
Intersection of intervals 10
Interval, arithmetic 11—14 17
Interval, extensions 21—24 34—36 41 44-50
Interval, extensions, mean value 45
Interval, extensions, of spline functions 24 103
Interval, extensions, of standard FORTRAN functions 23 24 41
Interval, extensions, of the class of functions used in computing 41
Interval, integrals 52
Interval, integration 52 56
Interval, majorants 69
Interval, matrices 11 59—62
Interval, metric 33
Interval, of functions 105
Interval, operators 69
Interval, polynomial enclosures 29 30
Interval, vectors 9
Inverse isotone operators 110
Jackson, L. W. 17 115
Jahn, K. — U. 56
Jones, S. 85
Kahan, W. 17
Kansy, K. 57
Kantorovich, L. V. 73
Kedem, G. 31
Kr ckeberg, F. 2 30 31 57 72 105 113 114 115
Krawczyk, R. 72 85 87 92
Krier, N. 17
Krier, N. and Spellucci, P. 17
Kuba, D. and Rail, L. B. 31
Kuhn — Tucker points 90—92
Kulisch, U. 31
Laveuve, S. E. 17
Linear algebraic systems 59—62 72
Linear programming 87—88
Lipschitz extensions 34—35 41 78 89 93
Lohner, R. and Adams, E. 115
| M-matrices 61
Machost, B. 87 92
Madsen, K. 73
Majorant see Interval majorant
Mancini, L. J. 92
Mancini, L. J. and McCormick, G. P. 92
Marcowitz, U. 7 112 113 115
Mathematical programming 87 92
Mathematical programming, convex programming 88—90
Mathematical programming, global optimization 92
Mathematical programming, linear programming 87—88
Mathematical programming, nonlinear optimization 90—92
Mean value form 45
Microprogramming 5 15
Midpoint of an interval 10
Midpoint of an interval, matrix 11
Midpoint of an interval, vector 10
Miller, W. 72
Minimum-maximum principle 102
Monotone operators 105—114
Monotonicity test form 46—48
Moore, R. E. 17 31 56 57 72 73 85 92 114 115
Moore, R. E. and Jones, S. 73 77 85
Muller’s lemma (application to) 113—114
n-body problem 99
Natural interval extensions 21 23
Net transfer 117
Neuland, W. 102 114
Newton step 78—79
Newton’s method 65 66—68 72
Nickel, K. 2 17 56 57 72 73 92 110 113 115
Nickel, K. and Ritter, K. 56
Nonlinear systems 62—68 72 75—85
Norm of an interval matrix 11
Norm of an interval vector 10
occurrences 42
Oliveira, F. A. 114
Olver, F. W. J. 17
Operator equations 69—72 93—115
Optimal multi-dimensional quadrature (application to) 84—85
Optimization see Mathematical programming
Ortega, J. M. and Rheinboldt, W. C. 73
Parter, S. V. 72 73
Partial differential equations 99 102—105 111—112 113
Partial differential equations, elliptic 102—105 112
Partial differential equations, parabolic 111—112 114
Picard iteration 72
Polytopes 17
Powers of intervals 23
Probability distributions 17
Push-down stack 77
Quasi-monotone operators 108
Rabinowitz, P. 84
Rail, L. B. 31 72
Rational interval functions 19—20 21
Ratschek, H. 7 17 45 56 57 72
Ratschek, H. and Schroeder, G. 57
Re-entry problem 113
Real restrictions 22
refinements 35 40—50
Richman, P. L. and Goldstein, A. J. 72
Richtmeyer, R. D. 2
Ris, F. N. 17
Robers, P. D. and Ben — Israel, A. 92
Robinson, S. 90 91 92
Rokne, J. 31
Rounded interval arithmetic 14—16 17
Safe starting regions 75—85
Scheu, G. and Adams, E. 108 115
Schmitt, G. 7
Schr der, J. 113 115
Schroeder, G. 57
Search procedures 76—78
Sensitivity analysis (application to) 121 123
Set inclusion 10
Set valued mappings 19
Simplex method (application to) 87—88
Skelboe, S. 7 48 49 57
Skelboe’s algorithm 48—49
Spaniol, O. 17
Spline functions 24 103 112
Spreuer, H. 112 115
Stewart, N. F. 17 92 114 115
Stewart, N. F. and Davey, D. P. 17
Stopping criteria 38—40 88 90 97 120
Strother, W. 19 31 56
Subdistributivity 13
Subset property 20
Symmetric intervals 14
Taylor series, interval remainder 25 29—30 54—56 95-97
Taylor series, recursive generation of Taylor coefficients 24—29 31 54—56 95—97 99
Test for existence 63
Three-valued logic 40
Tost, R. 105 114
Tri-diagonal matrices 83
Triplex — Algol 17 50
Two-point boundary value problems 71—72 83—84 100—102 113
Unbounded intervals see Extended interval arithmetic
Uncertainty in initial data 2
Uniform subdivisions 35
Union of intersecting intervals 10
United extensions 19 20 23 41
Van der Pol’s equation 99
Vergrberung see Degree reduction
Volterra’s model of conflicting populations 94
von Neumann, J. and Goldstine, H. 61 72
Wauschkuhn, U. 97 114
Width of an interval 10
Width of an interval matrix 11
Width of an interval vector 10
Wisskirchen, P. 56 72
Wongwises, P. 72
World Bank 119
Wrapping effect 97—99
Yohe, J. 17 31
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