### Table 3: Solving linear equations

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### Table 2: Bounds on the number of solutions of the FKP for a robot with planar platform (9 unknowns) When there are more than 3 sensors (we always assume that the sensors are not redundant, which means that they actually give information), it is not interesting to build the dialytic matrix. Indeed it is better to solve the non-linear system by taking advantage of its structure when the linear equations have been eliminated. We obtain in this way a better bound. If 6 sensors are used and give information, we obtain a unique solution by solving the linear system corresponding to the 6 equations of type IV given by the sensors and the 3 equations of type III. The cpu times given in Table 3 are the times we needed to obtain the bound with the symbolic method of Section 3.3. They are only indicative. In fact in practice this computation is not done since we only want to compute numerically the result.

"... In PAGE 26: ... Sensors 3 2 1 Before linear elimination 28 After linear elimination 10 15 21 Table 1: Number of monomials present in the equations before and after the resolu tion of the linear equations 5.1 Planar platform Table2 gives bounds on the number of solutions, depending on the number of extra sensors that are added on the robot. They also give the number of unknowns in the initial non-linear system, the number of equations in the square system obtained by... ..."

### Table 6. Performance comparison on linear equation solver.

"... In PAGE 9: ... CRA V apos;s SCILIB provides a routine for matrix inversion, which runs at 300 to 400 MFLOPS. The times reported in Table6 for the X-MP, however, are optimal. The linear equation solver used on the X-MP is using an out-of-core Gaussian elimination algorithm, based on block matrix-matrix products [Grimes 1988].... In PAGE 9: ... The linear equation solver was executed five times on both ma~ines. The remark- able result in Table6 is not so much the actual performance, but the considerable performance variation on the CRA Y -2. While all the routines varied about 15 to 35% in performance depending on system load, a 70% difference was noted in the linear equation solver.... ..."

### Table 4. LC axioms for linear equations and inequations

1998

"... In PAGE 9: ... Inequations are limited to one variable, and represented by : leq(x; ) for x and geq(x; ) for x The eq(x,v) constraint stands for :`x has current value v0 and is a placeholder for values of variables that evaluates its second argument. The LC rules8 for linear equations and inequations are given in Table4 . They are designed to maintain the system of equations in Gauss normal form and deduce the corresponding coe cients so that agents may access them.... ..."

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### Table 1: Performance of the Linear Equation Solver Application

"... In PAGE 17: ... To simulate moderate load, idle periods are between four and eight minutes and busy periods are from 20 to 30 minutes. The results of performance tests run using the linear equation solver application to solvea system of 1024 equations are shown in Table1 . The table shows the degradation which results when just two other processes per node are competing for computing resources.... ..."

### Table 3.1 Linear equation, = 1.

1995

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### TABLE 3 RESULTS FOR SYSTEMS OF LINEAR EQUATIONS

1973

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### Table 2: System of Linear Equations for calculating CYCACZCY

2002

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### Table 1. Matrix and set of linear equations corresponding to the

1995

Cited by 1

### Table 1: Performance of the Linear Equation Solver Application Execution time

"... In PAGE 17: ... To simulate moderate load, idle periods are between four and eight minutes and busy periods are from 20 to 30 minutes. The results of performance tests run using the linear equation solver application to solve a system of 1024 equations are shown in Table1 . The table shows the degradation which results when just two other processes per node are competing for computing resources.... ..."