Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Demidovich B.P., Maron I.A. — Computational Mathematics
Demidovich B.P., Maron I.A. — Computational Mathematics

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Computational Mathematics

Авторы: Demidovich B.P., Maron I.A.

Аннотация:

The basic aim of this book is to give as far as possible a systematic and modern presentation of the most important methods and techniques of computational mathematics on the basis of the general course of higher mathematics taught in higher technical schools. The book has been arranged so that the basic portion constitutes a manual for the first.cycle of "studies in approximate computations for higher technical colleges. The text contains supplementary material which goes beyond the scope of the ordinary college course, but the reader can select those sections which interest him and omit any extra material without loss of continuity. The chapters and sections which may be dropped out in a first reading are marked with an asterisk.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 688

Добавлена в каталог: 26.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Abel, Euler — Abel transformation      210
Abel, N.H., Euler — Abel method      209
Abramov, A.A.      114 676
Absolute error      19
Absolute value of a matrix      242
Absorbing barrier      667
Acceleration of convergence of Fourier trigonometric series by Krylov's method      217
Acceleration of convergence of numerical series      203
Acceleration of convergence of power series by Euler — Abel method      209
Acceleration of convergence of series      89
Accumulation, method of      306 640
Accuracy in determination of arguments from a tabulated function      48
Accuracy of quadrature formulas      618
Accuracy, estimation of      17
Additive inverse of a matrix      232
Adjoint of a matrix      236
Algebra, fundamental theorem of      162
Algebra, matrix      229
Algebraic equations, approximate solution of (special techniques for)      162ff
Algebraic equations, bounds of real roots of      167
Algebraic equations, general properties of      162ff
Algebraic volume      656
Algorithm, Euclid's      165
Algorithm, Hero's      107
Alternating sums, method of      169
Analysis, classical      5
Analytic functions, computing values of      89
Angle between two vectors      345
Approximate differentiation      574ff
Approximate differentiation, formulas of, based on Newton's first interpolation formula      575
Approximate differentiation, formulas of, based on Stirling's formula      580
Approximate integration      590ff
Approximate numbers      19ff
Approximate solution of algebraic equations, special techniques for      162ff
Approximation of improper integrals      633
Approximation, major      19
Approximation, minor      19
Approximation, trigonometric      225
Argument, principle of      166
Back substitution      280 see
Backward extrapolation      529
Backward interpolation      529
Barlow's tables      113
Baron, M.L.      321 648 677
Barrier, absorbing      667
Bases      see "Basis"
Basis (bases) of a space      340
Basis (bases) of a space, initial      341
Basis (bases), biorthogonal      391
Basis (bases), normalized orthogonal      346
Basis (bases), orthogonal      346
Basis (bases), orthonormal      346
Beckenbach, E.F.      321 506 674 675
Berezin, I.S.      321 458 645 675
Bernoulli method      198ff
Bernoulli numbers      99 208 625ff
Bernoulli numbers, generating function of      627
Bernstein, S.N.      608
Bessel's formula for parabolic interpolation      535
Bessel's function of order zero      582
Bessel's inequality      216
Bessel's interpolation formula      534 535
Bezikovich, Ya.S.      54 161 228 675
Bilinear expansion of a matrix      392
Bilinear form of a matrix      384
Biorthogonal bases      391
Biorthogonality relations      390 393
Biorthogonality, conditions of      390
Blocks of a matrix      256
Bordered matrices      257
Bordering, method of (matrices)      262
Bounds of real roots of algebraic equations      167
Bounds, method of      50
Bradis, V.M.      54 573 675
Brown, G.W.      674
Budan, theorem of Budan — Fourier      175 176
Bulgakov, B.V.      272 675
But, E.      506 675
Canonical convergents      59
Canonical norm of a matrix      243
Cardan's formula      186
Cauchy inequality      245
Cauchy test      83
Cayley — Hamilton theorem      397
Central derivatives, formulas for      580
Central differences      530
Central formulas      580
Central-difference formulas      531
Chain law      668
Chain, discrete Markov      667
Change-of-basis matrix      348
Characteristic determinant      376 565
Characteristic equation      376
Characteristic matrix      376
Characteristic number      375 377
Characteristic polynomial      376 382
Characteristic root      375
Chebyshev polynomial      554
Chebyshev's quadrature formula      607ff
Chebyshev, P.L.      554
Check sums      281
Check, final      17
Check, intermediate      17
Chords, method of      122
Class, periodicity      214
Classical analysis      5
Coefficients, Cotes      594 600
Coefficients, Fourier      213
Coefficients, Lagrangian      543
Collar, A.R.      272 675
Column vector      229
Combination method      136
Commutative matrices      234
Complex roots, one pair of      190
Complex roots, two pairs of      194 197
Components of continued fractions, terms of      55
Computation sheets      16
Computation work, rules of      15ff
Computation(s)      see also "Computing"
Computation(s) in which errors are not taken into exact account      42
Computation(s) of determinants      269
Computation(s), double, method of      50
Computational scheme of Danilevsky's method      416
Computing      see also "Computation"
Computing, analytic functions      89
Computing, cube roots      112
Computing, exponential functions      91
Computing, forms      16
Computing, functions      77ff
Computing, hyperbolic functions      101
Computing, logarithmic functions      95
Computing, polynomials      77
Computing, rational fractions      82
Computing, reciprocals      104
Computing, reciprocals of square roots      111
Computing, square roots      107
Computing, trigonometric functions      98
Conditions of biorthogonality      390
Conditions, Hurwitz      406
Conditions, Sylvester      389
Conformal partitioned matrices      257
Continued fraction(s)      55
Continued fraction(s), components of      55
Continued fraction(s), conversion of to a simple fraction      56
Continued fraction(s), expanding functions into      72ff
Continued fraction(s), infinite      55
Continued fraction(s), n-component      55
Continued fraction(s), nonterminating      66
Continued fraction(s), nonterminating, convergent      66
Continued fraction(s), nonterminating, divergent      67
Continued fraction(s), simple      56
Continued fraction(s), standard      56
Continued fraction(s), theory of      55f
Contraction mapping      487ff
Convergence of Fourier trigonometric series (acceleration of by Krylov method)      217
Convergence of iteration processes for systems of linear equations      322ff 394ff
Convergence of iteration processes for systems of linear equations, necessary and sufficient conditions for      398
Convergence of iteration processes for systems of linear equations, sufficient conditions for      322
Convergence of iteration processes, first sufficient condition of      491
Convergence of iteration processes, second sufficient condition of      493
Convergence of matrix power series      394
Convergence of numerical series, accelerating      203
Convergence of power series, acceleration of by Euler — Abel method      209
Convergence of Seidel process for a normal system      403
Convergence of Seidel process, first-sufficient condition for      327
Convergence of Seidel process, necessary and sufficient conditions for      400
Convergence of Seidel process, second sufficient condition for      330
Convergence of Seidel process, third sufficient condition for      333
Convergence of series, acceleration of      89
Convergence of the Newton process      465 469
Convergence of the Newton process, rapidity of      474
Convergence of the Newton process, stability of      478
Convergence theorem      214
Convergence, accelerating (by Lyusternik method)      453 458
Convergence, methods for effectively checking the conditions of      405
Convergent integral      633 635
Convergents      58ff
Convergents, canonical      59
Convergents, law of formation of      59
Coordinates of a vector      336
Coordinates of a vector in a basis      341
Correct digit      25
Cotes coefficients      594 600
Cotes, Newton — Cotes formulas      599
Cotes, Newton — Cotes quadrature formulas      593
Cramer's formulas      276
Cramer's rule      273
Cubafure formulas      590 641ff
Cubafure formulas of Simpson type      644
Cubafure formulas, Simpson's      644
Cubature, mechanical      590
Cube roots, computation of      112
Danilevsky, A.M., method of      412
Danilevsky, computational scheme of      416
Danilevsky, exceptional cases in      418
Danilevsky, method of, computation of eigenvector's by      420
Davis, P.      674 675
De La Vallee-Poussin, C.J.      228 677
Degenerate linear transformation      374
DEL      497
Delta, Kronecker      230
Delta, the operator $\Delta$      508
Derivatives, central      580
Derivatives, partial      588
Descartes' Rule of Signs      178
Descent, steepest      496 499 see
Determinant(s)      230
Determinant(s), characteristic      376 565
Determinant(s), computation of      269
Determinant(s), Gaussian method in computing      288
Determinant(s), secular      376 565
Determinant(s), secular, expansion of      410ff 429
Determinant(s), Vandermonde      592 614
Diagonal difference table      511
Diagonal matrix      229 265
Difference equation      198
Difference table      510
Difference table, diagonal      511
Difference table, horizontal      511
Difference(s), central      530
Difference(s), divided      554ff
Difference(s), double (of higher order)      570
Difference(s), error of      34
Difference(s), finite      507ff
Difference(s), lambda ($\lambda$-difference)      440
Differentiation operator      629
Differentiation, approximate      574ff
Differentiation, graphical      586
Differentiation, Numerical      583
Digit, correct      25
Digit, significant      24
Dimensionality of a subspace      342
Direct procedure      280 see
Discrete Markov chain      667
Distribution function      651
Distributivity      344
Divergent integral      633 635
Divided differences      554ff
Divided differences, table of      556
Double computation, method of      50 622
Double differences of higher order      570
Double-entry table      569
Duncan, W.J.      272 675
Eigenvalue(s)      375 377 382 445
Eigenvalue(s), extremal property of      387
Eigenvalue(s), finding (of a matrix)      410ff
Eigenvalue(s), finding the first      436
Eigenvalue(s), finding the numerically largest      430
Eigenvalue(s), finding the second      439
Eigenvector(s)      375 382 445ff
Eigenvector(s), computation of by Danilevsky's method      420
Eigenvector(s), computation of by Krylov's method      424
Eigenvector(s), finding      410ff 430 439 see
Element(s) of a matrix      229
Element(s), principal      287
Emde      524 568
Empirical formula      524
Entries (of a matrix)      229
Equal effects, principle of      45
Equation(s), algebraic      162
Equation(s), characteristic      376
Equation(s), difference      198
Equation(s), equivalent      119
Equation(s), graphical solution of      119
Equation(s), linear      273
Equation(s), nonlinear      459 see
Equation(s), root of      115ff
Equation(s), secular      376
Equation(s), solution of      199
Equivalent equations      119
Equivalent matrices      268
Error estimate, probability      52
Error(s)      19
Error(s) of a difference      35
Error(s) of a product      37
Error(s) of a quotient      40
Error(s) of a sum      33
Error(s) of method      22 621
Error(s) of operation      23 84
Error(s) of the problem      22
Error(s), absolute      19
Error(s), computations in which errors are not taken into exact account      42
Error(s), epsilon ($\varepsilon$-error) (propagation law of)      515
Error(s), general formula for      42
Error(s), initial      23
Error(s), limiting absolute      20
Error(s), limiting relative      21
Error(s), relative      19 21 see
Error(s), residual      23
Error(s), rounding      23
Error(s), sampling      666
Error(s), sources of      22ff
Error(s), theory of      42
Escalator method      320
Euclid's Algorithm      165
Euler — Abel method      209
Euler — Abel transformation      210
Euler — Maclaurin formula      628 630
Euler — Maclaurin summation formula      630
Euler, L.      58
1 2 3 4
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте