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Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
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Fritz J. - Lectures on advanced numerical analysis |
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Предметный указатель |
Accelerated iteration schemes 22
Accumulated roundoff error 96
Accumulated truncation error 96
Accumulated truncation error for symmetric hyperbolic system 155
Analytic continuation 87
Analytic functions, zeros of 58
Bernoulli's method 46
Bernstein formula 91
Characteristic equation of a difference equation 46
Characteristic equation of a matrix 58
Characteristic form of hyperbolic system 157
Characteristics of the wave equation 129
Chebyshev polynomials 84
Chebyshev polynomials, expansion in 93
Convergence of interpolation polynomials 87
Cramer's rule 1 32 33
Derivative, difference approximations for 97
Determinant 1
Difference approximation for the heatequation 108
Difference approximations for derivative 97
Difference equation 46 94
Difference equation, fundamental solution of 100
Difference equation, inhomogeneous 100
Difference equation, maximum principle for 125
Difference schemes, refined 97
Difference schemes, stable 99 111
Difference schemes. 'explicit' 124
Difference, divided 82
Dirichlet problem 163
Dirichlet problem, error estimates for 166
Divided difference 82
Domain of dependence 109 130
Duhamel's principle 100
Eigenvalues of matrices 58 70
Eigenvalues of matrices, iteration schemes for 75
Eigenvectors, estimates for 72
Elimination method for matrix inversion 32
Elliptic equation 163
Equations, systems of 60
Error estimates for the Dirichlet problem 166
Euclid's Algorithm 44
Euler Polygon Method 94
Expansion in Chebyshev polynomials 93
Forward differences 94
Fourier integral 132
Fundamental solution of difference equation 100
Gauss - Seidel scheme 19
Gershgorin theorem 70
Gradient methods 24
Gradient methods of Hestenes - Stiefel 29
Graeffe root-squaring process 53
Graeffe root-squaring process, applied to eigenvalues of a matrix 58
Heat equation 106
Heat equation, difference approximations 108
Heat equation, implicit scheme for the 124
Heat equation, initial value problem 107
Heat equation, maximum principle for the 110 122
Heat equation, reflection principle for the 124
Hermitian matrix 12
Hestenes - Stiefel Conjugate Gradient Method 29
Hyperbolic equation 129
Hyperbolic equation, second order 147
Hyperbolic system 158
Hyperbolic system in two independent variables 157
Hyperbolic system, characteristic form of 157
Hyperbolic system, stability condition for 160
Implicit scheme for the heat equation 124
Inhomogeneous difference equation 100
Interpolation formula, Lagrange's 80
Interpolation formula, Newton's 81
Interpolation formula, Remainder term in 83
Interpolation polynomials 80
Interpolation polynomials, convergence of 87
Iteration schemes, accelerated 22
Iteration schemes, accelerated for eigenvalues 75
Iteration schemes, accelerated for solving equations 60
| Jacobi method 73
Lagrange interpolation polynomials 80
Laplace equation 163
Lehmer method 56
Linear system in characteristic form 158
Lipschitz condition 61
Matrix 11
Matrix inversion, elimination method 32
Matrix inversion, elimination method by successive approximations 16
Matrix, characteristic equation of 58
Matrix, eigenvalues of 58
Matrix, hermitian 12
Matrix, natural norms for 11
Matrix, norm of the reciprocal of 14
Matrix, trace of 13 58
Matrix, unitary 12
Maximum principle 115
Maximum principle for difference equation 125
Maximum principle for heat equation 110 122
Maxwell's equations 145 146
Maxwell's equations for matrices 11
Natural norms for matrices 11
Natural norms for vectors 7
Newton's interpolation formula 81
Newton's method 67
Norm 2 5
Norm of a matrix 5
Norm of the reciprocal of a matrix 14
Norm, natural for matrices 11
Norm, natural for vectors 7
Parseval's theorem 135
Polygon method 97
Polynomials, common zeros of two real 44
Polynomials, interpolation 80
Polynomials, real zeros of 36
Quasi-linear system 157
Refined difference schemes 97
Reflection principle for the heat equation 124
Remainder term in interpolation formula 83
Root as limits of rational expression, Lehmer method 56
Root of an analytic function 52
Root of two real functions 39
Root, largest 46
Root-squaring process, GraefFe 53
Rouche's theorem 42
Roundoff error 95
Roundoff error, accumulated 96
Sobolev's lemma 153
Stability 98 112
Stability of difference scheme 99 111
Stability, condition for hyperbolic systems 160
Stability, condition for symmetric hyperbolic systems 148
Stirling's formula 90
Sturm's method 36
Successive approximations 18 19
Successive approximations, matrix inversion by 16
Symmetric hyperbolic system 143 145
Symmetric hyperbolic system, accumulated truncation error 155
Symmetric hyperbolic system, stability condition for 148
Systems of equations 60
Taylor's formula as limit 84
Trace of matrix 13 58
Trigonometric interpolation 91
Trigonometric polynomials 91
Truncation error 96 97
Truncation error, accumulated 96
Unitary matrix 12
Unstable 97
Wave equation in one dimension 129 138
Wave equation, characteristics of 129
Wave equation, initial value problem 129
Zeros of a polynomial in half-plane 45
Zeros of a real polynomial 36
Zeros of analytic functions 38 58
Zeros of two real polynomials, common 44
'Explicit' difference schemes 124
'Characteristic' direction 158
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