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Fritz J. — Lectures on advanced numerical analysis
Fritz J. — Lectures on advanced numerical analysis

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Название: Lectures on advanced numerical analysis

Автор: Fritz J.


These Lectures on Numerical Analysis are essentially lectures notes of a course on "Advanced Numerical Methods" which the author gave in 1956-57 at the Institute of Mathematical Sciences at New York University. The original notes, prepared by S. d'Ambra and S. Locke, were distributed by the Institute for a number of years in mimeographed form. The author has made extensive revisions in the wording of theorems and proofs and the list of references, but had to refrain from making the major changes that would be required in an attempt to bring the material up to date. It has not always been possible to perfect the informal style of the original notes.
It is hoped that even in its present form the book can serve as an introduction to the field for students who have a fair knowledge of linear algebra, of functions of a complex variable, and of the basic facts about ordinary and partial differential equations.

Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1966

Количество страниц: 179

Добавлена в каталог: 23.02.2005

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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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