scholarly journals Fast direct solution methods for symmetric banded Toeplitz systems, based on the sine transform

2002 ◽  
Vol 343-344 ◽  
pp. 211-232
Author(s):  
Jef Hendrickx ◽  
Marc Van Barel
1981 ◽  
Vol 35 (1) ◽  
pp. 37-51
Author(s):  
Franz Steidler

The question of which algorithm is most appropriate for the solution of normal equations with different structures has been investigated. The solution methods are a direct solution for banded and banded-bordered matrices, a special direct solution technique for arbitrary sparse systems of equations and the method of conjugate gradients. The algorithms have first been applied to photogrammetric bundle adjustment with self-calibration, which leads to a banded-bordered matrix of the normal equations, and secondly to calculations of digital height models that are generated by a simple version of the method of finite elements and which lead to band matrices.


AIAA Journal ◽  
1989 ◽  
Vol 27 (10) ◽  
pp. 1459-1461 ◽  
Author(s):  
C. P. van Dam ◽  
M. Hafez

1967 ◽  
Vol 21 (2) ◽  
pp. 345-352 ◽  
Author(s):  
Milton E. Rosenbaum ◽  
Sidney J. Arenson

In 2 experiments female Ss observed a confederate solve 6 “water-jar” problems. Each problem permitted 2 modes of solution. In Exp. I the 3 conditions were observation of direct solutions, indirect solutions, or a mixture of both. In subsequent performances on similar problems, observers adopted the solution methods that had been observed even when inefficient. In Exp. II the order of the jar capacities was varied to test for the acquisition by observation of a more general solution set. The 3 conditions were observation of indirect solutions, direct solutions, or no observation (control). The results for both method of solution adopted and time for solution indicate that observation of the direct solution did not facilitate problem solving, but observation of the indirect solution did hinder this activity.


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