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By Hasegawa F., Hashima M., Kanda Sh.

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Additional info for A Stereo Vision System for Position Measurments and Recognition in an Autonomous Robotic System for Carrying Food Trays

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Is there another way to solve quadratic equations such that we can confidently obtain a small relative error in the result? Look at the calculation for x1 closely and you will notice that two numbers of exceedingly close values are being subtracted from each other. 5, this naturally has disastrous consequences on the result. If we prevent this subtraction step from occurring, we can obviate the problem of subtractive cancellation. 6) will always result in a subtraction of two numbers in the numerator.

Write a MATLAB program to convert a decimal fraction into its equivalent binary fraction. 2. Verify the correctness of your algorithm from the answers in the chapter. 2. (i) Determine the 4-bit significand (binary fraction) for the following decimal fractions: (a) 1=9, (b) 2=3. 1. (ii) Add the 4-bit binary significands determined in (i) to find the binary equivalent for ð1=9Þ þ ð2=3Þ. When performing binary addition, note these simple rules: 0 + 1 = 1 and 1 + 1 = 10. 3. 4. 5. 6. (iii) Convert the 4-bit binary significand determined in (ii) to its decimal equivalent.

If a zero of the function is being sought, then the approach of the function towards zero can be the test for termination of the iterative method, such as jfðxi Þj5E; where E is the tolerance limit close to zero. Finally, other checks can be used to ensure that the algorithm is functioning properly and whether, in certain situations, convergence is not reached in an acceptable time limit, in which case the algorithm can be terminated. Iteration checks that are inserted into computational procedures to prevent an endless iterative loop include capping the total number of iterations allowed and placing bounds on the magnitude of the iteration variables or the function values being calculated.

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