Computing Methods, Volume 2Computing Methods, Volume I generalizes and details the methods involved in computer mathematics. The book has been developed in two volumes; Volume I contains Chapters 1 to 5, and Volume II encompasses Chapters 6 to 10. |
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Page 29
... vectors forms the basis for the lowest linear manifold containing the vectors ( 0 ) , AF ( 0 ) , Ak ( 0 ) . The vector 7 ( k + 1 ) , being orthogonal to all the vectors of the basis , will also be orthogonal to all the linear manifold ...
... vectors forms the basis for the lowest linear manifold containing the vectors ( 0 ) , AF ( 0 ) , Ak ( 0 ) . The vector 7 ( k + 1 ) , being orthogonal to all the vectors of the basis , will also be orthogonal to all the linear manifold ...
Page 195
... vector C1 = Aco - α10co ( 1 ) is orthogonal to the vector co . This is always possible and the condi- tion of orthogonality gives α10 ( Ačo , čo ) ( čo , čo ) ( 2 ) It may be that č1 = 0. In this case the vectors co and Ac 。 are li ...
... vector C1 = Aco - α10co ( 1 ) is orthogonal to the vector co . This is always possible and the condi- tion of orthogonality gives α10 ( Ačo , čo ) ( čo , čo ) ( 2 ) It may be that č1 = 0. In this case the vectors co and Ac 。 are li ...
Page 255
... vector AP , thus approximates more and more to the vector e ( i ) in direction with increasing p provided a 0. It is a similar case with the rest of the components ; of the vector v . The following conclusions can be drawn from the ...
... vector AP , thus approximates more and more to the vector e ( i ) in direction with increasing p provided a 0. It is a similar case with the rest of the components ; of the vector v . The following conclusions can be drawn from the ...
Contents
The Squareroot Method | 16 |
Conjugate Gradients | 23 |
Partitioning into SubMatrices | 34 |
Copyright | |
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a₁ absolute magnitude approximate solution arbitrary b₁ boundary conditions boundary nodes boundary value problem C₁ C₂ calculations Cauchy problem characteristic polynomial coefficients column consider constant convergence corresponding defined derivatives difference equation difference scheme differential equations Dirichlet problem dx dy eigenvalues eigenvectors elements equal error estimate exact solution find the solution formula Goursat problem inequality initial conditions initial vector integral equation internal nodes interval iteration J²u K(xn k₁ linear algebraic linear algebraic equations matrix mesh method method of solving multiplied norm obtained operator orthogonal Poisson's equation presupposed real roots region G right-hand side sequence set of equations set of linear straight line Substituting Suppose we put symmetric Taylor formula theorem U₁ vector x₁ y₁ zero ду дх მყ