1. This paper presents a new method named "Analytic Orthogonalization", for orthogonalizing direction cosine matrix.

2. This paper introduces a Grain - Schmidt cascade orthogonalization preprocessor decor - relating the received signals in adaptive array.

3. Since it involves no procedure of orthogonalization, the method makes calculation much simpler than that of conventional ones.

4. Orthogonalization method of simultaneous estimation of polynomial model order and parameter is presented in this paper.

5. The reason for deteriorated performance of conventional orthogonalization algorithms for adaptive jamming cancellation at low jamming to noise ratio (JNR) was analyzed.

6. Based on the idea of the Schmidt orthogonalization and the orthogonal chaotic carriers being generated, a chaos-based quadrature modulation communication system is proposed and realized.

7. The Successive Orthogonalization Decentralized Kalman Filter (SODKF ) is a new method which is used for large system state estimation.

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8. Calculations show that Analytic Orthogonalization has the advantages of high accuracy of orthogonalization. and light labour of calculation.

9. Based on this relation, boundary orthogonalization can be achieved by the search method of stepwise extension and the bisection algorithm with iterative methods in solving equations.

10. Deformation of flexible legs is defined by mode synthesis method, and the principle of mode selection and orthogonalization during modeling are discussed.

11. This paper proposes an orthonormalization method which can get the same theoretical orthonormal results with the traditional Gram-Schmidt orthogonalization process for skinny (long) matrices.

12. GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs.

13. The error of this method is analyzed. A comparison is made between Analytic Orthogonalization and Iterative Optimal Orthogonalization.

14. The advantage of the method lies in employing a new basic function and avoiding to the Schmidt orthogonalization.

15. Theory and application of systems of linear equations, linear independence, linear transformations, inverse of a matrix, determinants, vector spaces, eigenvalues, eigenvectors , and orthogonalization.

16. Using the program to generate 3-D multi-block abutting structured grid of reverse jet flow field with the controlling of concentration and orthogonalization.

17. For the requirement of applications, a new PCMS improved by using an optimal Gram Schmidt orthogonalization method is proposed.

18. A new computational method for inverse matrices is obtained based on Schmidt orthogonalization.

19. The conclusion is given through simulation that the overall principle to optimization is orthogonalization of the sensitivity optimal vector.