Computational Mathematics in Engineering |
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Page 195
... λι = 0 X2 = 0 F + L = 0 Из = 8 U1 = 10 ( 7.78 ) with the rest of the variable equaling zero . The third iteration will result in x2 = 2 λι = 3.2 F + L = -4 λε = 6.4 Из = 10 And , similarly , the fourth iteration is ( 7.79 ) x1 = 6 x2 ...
... λι = 0 X2 = 0 F + L = 0 Из = 8 U1 = 10 ( 7.78 ) with the rest of the variable equaling zero . The third iteration will result in x2 = 2 λι = 3.2 F + L = -4 λε = 6.4 Из = 10 And , similarly , the fourth iteration is ( 7.79 ) x1 = 6 x2 ...
Page 208
... λι + • ( 8.31 ) Note that the convergence of this method is proportional to 2k instead of k . Thus , formation of scalar products cuts the iteration by almost one- half . In the case of symmetrical matrices since A ' = A , this method ...
... λι + • ( 8.31 ) Note that the convergence of this method is proportional to 2k instead of k . Thus , formation of scalar products cuts the iteration by almost one- half . In the case of symmetrical matrices since A ' = A , this method ...
Page 211
Shahen A. Hovanessian. P - 1AP λι ( a 12 / x1 ) ( a13 / x1 ) = 0 A 22 ( X2 / X1 ) α12 a23- ( x2 / x1 ) α13 0 A32 - A33 ( X3 / X1 ) α12 33 ( X3 / X1 ) a 13 / ― - ( 8.41 ) λι b12 b13 = 0 0 B where variables b12 , b13 , and matrix B are ...
Shahen A. Hovanessian. P - 1AP λι ( a 12 / x1 ) ( a13 / x1 ) = 0 A 22 ( X2 / X1 ) α12 a23- ( x2 / x1 ) α13 0 A32 - A33 ( X3 / X1 ) α12 33 ( X3 / X1 ) a 13 / ― - ( 8.41 ) λι b12 b13 = 0 0 B where variables b12 , b13 , and matrix B are ...
Contents
Numerical Evaluation of Matrices and Simulta | 1 |
Choleskis Method | 7 |
Illconditioned Matrices | 19 |
Copyright | |
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a-ẞ tracker A₁ Assume calculate central difference characteristic vector coefficients column constraints convergence corresponding D₁ data points defined Denoting derivative diagonal difference operator differential equation Digital Computer Methods digital filter elements equa error estimate evaluated expected value exponential distribution F₁ Figure finite difference Formulate the solution Fourier series Fourier transform frequency function F G₁ Gaussian given Hovanessian initial vector input inverse k₁ Kalman filtering Lagrangian least-squares linear programming McGraw-Hill multipliers Note number of data Obtain the values optimization P₁ parameters percent polynomial probability density function quadratic programming random numbers recursive represents result second characteristic value set of equations similarity transformation simultaneous equations solve step symmetrical symmetrical matrix Table Taylor series Theorem three iterations tion values and vectors variable W⁰ x₁ y₁ Y₂ Yi+1 Yn+1 York zero λ₁ λι