Selected Articles on Numerical Analysis: Translated [from the Russian]1949 |
From inside the book
Results 1-3 of 10
Page 9
... bilinear one . The value of the norm in both cases is one and the same . We adduce exam- ples of bilinear operations . Example 1. Let us consider the bilinear operation sending the space X = m into Y = m . It is easily seen that it has ...
... bilinear one . The value of the norm in both cases is one and the same . We adduce exam- ples of bilinear operations . Example 1. Let us consider the bilinear operation sending the space X = m into Y = m . It is easily seen that it has ...
Page 10
... bilinear operation will be an operation of the form : ( 6 ) y = B ( x , x ' ) = WXXX ' One is readily satisfied that for such where w is a complex number . an operation ( 7 ) JB | = | W | Example 4. An example of a bilinear operation ...
... bilinear operation will be an operation of the form : ( 6 ) y = B ( x , x ' ) = WXXX ' One is readily satisfied that for such where w is a complex number . an operation ( 7 ) JB | = | W | Example 4. An example of a bilinear operation ...
Page 12
... bilinear operation . In conformity with this , by P ' ( x ) and || P " ( x ) || should be understood the norms , taken res- pectively in the spaces ( XY ) and [ X → ( X- > Y ) ] . ( See M. K. Gavurin , [ 17 ] . ) We will note some ...
... bilinear operation . In conformity with this , by P ' ( x ) and || P " ( x ) || should be understood the norms , taken res- pectively in the spaces ( XY ) and [ X → ( X- > Y ) ] . ( See M. K. Gavurin , [ 17 ] . ) We will note some ...
Common terms and phrases
A₂ abscissas algebraic equations analogous application approximate solution bilinear boundary conditions C₂ coefficients complex numbers computations contour convergence of Newton's corresponding D₂ d³u(y de(x defined denote determination displacements element elliptic integrals equa estimate exact solution example fulfilled function u(x Gauss Gauss's formula given inequality initial value integral equation integrand interpolation interval inverse Let us consider linear operation matrix method of lines Newton's method Newton's process nodes nonlinear norm obtain odd function odd polynomial operation mapping operation sending ordinary differential equations orthogonal Ostrowski partial differential equations points polynomial of degree proper value proper vectors quadratic form quadrature formula quantities region relaxation method residual forces satisfy second derivative solution of system Southwell Southwell's space sphere successive approximations symmetric Theorem tion trigonometric polynomial x₁