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| Авторизация |
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| Herriot J.G. — Methods of mathematical analysis and computation |
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| Предметный указатель |
 operator 2 4
Adams' method 147
Adams' method, modified 148
Adjoint differential equation 130 131
Adjoint matrix 62 63 84
Aitken's  -process 100 101 105 106
Aitken, A.C. 95 96 101 103
Augmented matrix 66
Backward difference 8
Bairstow method 44—47
Bi-orthogonal system of vectors 110
Bilinear resolution of matrix 104
Birge — Vieta method 44
Canonical box 90
Cauchy's problem 174
Cayley — Hamilton theorem 83 84
cell 186
Central difference 12
Central-difference interpolation formulas 10—14
Characteristic equation of matrix 81 84
Characteristic function of matrix 80
Characteristic numbers of matrix 80 81
Characteristic numbers of matrix, calculation of 92—111
Characteristic polynomial of matrix 80 84
Characteristic vectors of matrix 80 81
Characteristic vectors of matrix, calculation of 92—111
Characteristics of wave equation 176
Closed formulas 29
Coefficients of double Fourier series, formulas for 168
Coefficients of Fourier series, formulas for 156
Cofactor 56
Column vector 53
Complementary function 121 124 136 163 164
Corrected value 139 145 148 152 153
Corrector formula 138 145 148 152 153
Cramer's rule 65
Crout method of elmination 73—79
Crout method of elmination, check column for 76
Deflation 92 103—107
Descartes' Rule of Signs 48
Determinant, evaluation of 56 76
Determinant, principal minor of 82
Diagonal matrix 62
Difference of factorial polynomial 5
Difference table 2 8 12
Difference, backward 8
Difference, central 12
Difference, forward 2
Difference, repeated 2 3 8 12
Differential equation 112
Differential equation, order 113
Differential equation, ordinary see "Ordinary differential equation"
Differential equation, partial see "Partial differential equation"
Dirichlet's problem 173
Dirichlet, theorem of 157
Discriminant of quadratic form 88
Double Fourier series 168—171
Double Fourier series, formulas for coefficients of 168
Double Fourier series, half-range 169
E operator 4
Eigenvalues of matrix 81
Eigenvector of matrix 81
Elimination, Crout method of 73—79
Elliptic partial differential equation 174 175 186—190
Elliptic partial differential equation, finite-difference approximation for 186
Elliptic partial differential equation, stencil for 187
Equality, of matrices 55
Equality, of vectors 53
Error, in numerical differentiation formulas 32 33
Error, in numerical integration formulas 31 32
Error, in polynomial approximation 20 21
Euler's method for ordinary differential equation 118
Even function 157 160
Everett's interpolation formula 14
Exact ordinary differential equation 128 129
Explicit difference method for parabolic partial differential equation 181
Factorial polynomial 5
Factorial polynomial, difference of 5
False position, method of 36—39
Finite discontinuity 157
Finite-difference approximation, for elliptic partial differential equation 186
Finite-difference approximation, for hyperbolic partial differential equation 176
Finite-difference approximation, for parabolic partial differential equation 181 182
Forward difference 2
Fourier cosine series 162
Fourier series 155—172
Fourier series, application to solution of ordinary differential equations 162—165
Fourier series, application to solution of partial differential equations 165—168
Fourier series, double 168—171
Fourier series, formulas for coefficients of 156
Fourier series, half-range 161 162
Fourier sine series 161
Gauss — Jordan method of 71 72
Gauss — Jordan method of elimination 71 72
Gauss — Seidel iteration 79 80
Gauss's interpolation formula, backward 13
Gauss's interpolation formula, forward 11 12
Gauss's method of 67—71 183
Gauss's method of elimination 67—71 183
Givens' method, for general complex matrix 111
Givens' method, for real symmetric matrix 110
Green's function 135
Half-range double Fourier series 169
Half-range Fourier series 161 162
Hamilton — Cayley theorem 83 84
Hamming, R.W. 146
Heat conduction problem, in one dimension 174
Heat conduction problem, in two dimensions 171
Heat conduction problem, steady-state 172
Heat equation, Fourier series solution of 165—168
Hermitian form 89
Hermitian matrix 89
Higher-order ordinary differential equation 151—154
Hyperbolic partial differential equation 174 175—180
Hyperbolic partial differential equation, fininte-difference approximation for 176
Hyperbolic partial differential equation, stencil for 177
Identity matrix 62
Implicit difference method for parabolic partial differential equation 182
Indicial function 133
Initial-value problem 174
Inner product of vectors, complex components 86
Inner product of vectors, real components 54
Integrating factor for ordinary differential equation 128 130
Interpolating function 1
Interpolating polynomial 1
Interpolation 1—21
Interval of dependence 176
Inverse interpolation 19
Inverse matrix 62
Inverse matrix, calculation of 69 72 78
Iterative procedure for square root 41
Iterative process, order of 39 40
Jacobi method, for characteristic numbers 108
Jacobi method, variations of 109
Jordan canonical form of matrix 90
Jump discontinuity 131 157
Kronecker delta 15 57
Lagrange three-point interpolation, coefficients for 17
Lagrange's interpolation formula 15
Lagrangian coefficient function 15 17
Lanczos' method for reduction of matrix to tri-diagonal form 110
Laplace's differential equation 172 173
Latent roots of matrix 81
Latent vector of matrix 81
Lattice points 186
Left-hand limit 157
Length of vector 54
Lineal element 116
Linear differential equation 120—137
Linear differential equation, constant coefficients 120—125
| Linear differential equation, first order 127
Linear differential equation, second order 129
Linear equations 52—111
Linear transformation 57
Linearly dependent vectors 55
Linearly independent solutions of ordinary differential equations 121
Linearly independent vectors 55
Link of net 186
Lipschitz condition 119
Lower triangular matrix 68
Matrices, equality of 55
Matrices, similar 89
Matrices, sum of 55
Matrix 55
Matrix multiplication 57—61
Matrix polynomial 84
Matrix, bilinear resolution of 104
Matrix, characteristic equation of 81 84
Matrix, characteristic function of 80
Matrix, characteristic numbers of 80 81
Matrix, characteristic numbers of, calculation of 92—111
Matrix, characteristic polynomial of 80 84
Matrix, characteristic vectors of 80 81
Matrix, characteristic vectors of, calculation of 92—111
Matrix, diagonal 62
Matrix, eigenvalues of 81
Matrix, eigenvector of 81
Matrix, hermitian 89
Matrix, identity 62
Matrix, inverse of 62
Matrix, inverse of, calculation of 69 72 78
Matrix, Jordan canonical form 90
Matrix, latent roots of 81
Matrix, latent vector of 81
Matrix, lower triangular 68
Matrix, minimum polynomial of 85
Matrix, nonsingular 62
Matrix, orthogonal 64
Matrix, power of 83
Matrix, principal diagonal of 62
Matrix, proper numbers of 81
Matrix, proper values of 81
Matrix, proper vector of 81
Matrix, rank of 66
Matrix, reduction to tri-diagonal form 110
Matrix, secular equation of 81
Matrix, singular 62
Matrix, spectrum of 81
Matrix, square 55
Matrix, symmetric 61
Matrix, trace of 82
Matrix, transpose 61 86
Matrix, tri-diagonal 110 111 183
Matrix, unit 62
Matrix, upper triangular 68
Mesh of net 186
Milne and Reynolds 146
Milne's method 145—147
Milne's method for second-order differential equation 152—154
Milne's method for systems of differential equations 151 152
Minimum polynomial of matrix 85
Minor 56
Modified Adams' method 148
Multiplication of matrix, by matrix 57—61
Multiplication of matrix, by scalar 56
Newton — Raphson method 39—44
Newton's backward-difference formula 7—10
Newton's forward-difference formula 4—7 10
Newton's three-eighths rule 28 32 146
Node of net 186
Nonsingular matrix 62
Numerical differentiation 22—25 32 33
Numerical integration 22 25—32
Numerical solution of ordinary differential equations 117 137—154
Numerical solution of partial differential equations 173—190
Odd function 157
Open formulas 29
Operator 2 4
Operator E 4
Ordinary differential equation 112—154
Ordinary differential equation, Adams' method 147
Ordinary differential equation, Adams' method, modified 148
Ordinary differential equation, adjoint equation 130 131
Ordinary differential equation, application of Fourier series to solution of 162—165
Ordinary differential equation, auxiliary equation 121
Ordinary differential equation, complete 120
Ordinary differential equation, direction field 116
Ordinary differential equation, Euler's method 118
Ordinary differential equation, exact 128 129
Ordinary differential equation, existence theorem 119
Ordinary differential equation, first-order 137
Ordinary differential equation, general solution of 114
Ordinary differential equation, graphical solution of 116
Ordinary differential equation, higher-order 151—154
Ordinary differential equation, homogeneous 120
Ordinary differential equation, integral curve of 116
Ordinary differential equation, integrating factor 128 130
Ordinary differential equation, isocline 116
Ordinary differential equation, linear 120—137
Ordinary differential equation, linear, constant coefficients 120—125
Ordinary differential equation, linear, first-order 127
Ordinary differential equation, linear, second-order 129
Ordinary differential equation, linearly independent solutions of 121
Ordinary differential equation, Milne's method 145—147 151—154
Ordinary differential equation, modified Adams' method 148
Ordinary differential equation, nonhomogeneous 120
Ordinary differential equation, numerical solution of 117 137—154
Ordinary differential equation, particular solution of 114
Ordinary differential equation, reduced 120
Ordinary differential equation, Runge — Kutta method 149—151
Ordinary differential equation, solution of 114
Ordinary differential equation, solution of, by graphical procedure 116
Ordinary differential equation, stability problem 146
Ordinary differential equation, starting solution of 140—145
Ordinary differential equation, variation of parameters, method of 125—127
Ordinary differential equations, system of 113 151 152
Orthogonal matrix 64
Orthogonal vectors 54
Overrelaxation 188
Parabolic partial differential equation 174 175 180—186
Parabolic partial differential equation, explicit method for 181
Parabolic partial differential equation, finite-difference approximation for 181 182
Parabolic partial differential equation, implicit method for 182
Parabolic partial differential equation, stability of numerical solution 181 182
Parabolic partial differential equation, stencil for explicit method 181
Parabolic partial differential equation, stencil for implicit method 182
Partial differential equation 112 165—172 173—190
Partial differential equation, application of Fourier series to solution of 165—172
Partial differential equation, elliptic 174 175 186—190
Partial differential equation, hyperbolic 174 175—180
Partial differential equation, numerical solution of 173—190
Partial differential equation, parabolic 174 175 180—186
Partial differential equations, classification of 1^4
Periodic function 155
Piecewise continuous function 131
Polynomial equations, solution of 42—51
Positive definite quadratic form 88
Power method 92 93—103
Power method, acceleration of convergence 100 102
Power of matrix 83
Predicted value 139 145 148 151 152
Predictor formula 138 145 148 151 152
Predictor-corrector method 139 140 145 148 151—154
Principal diagonal 62
Principal minor of determinant 82
Proper numbers of matrix 81
Proper values of matrix 81
Proper vector of matrix 81
Quadratic form 88
Quadratic form, discriminant of 88
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