201 Exam Part A. (32 points) Answer 8 of the following 9 questions. Only the fir

Question

201 Exam Part A. (32 points) Answer 8 of the following 9 questions. Only the first 8 questions will be marked 1. (4 points) What are truncation errors? How did they get their name? 2. (4 points) Define accuracy and precision. How do they differ? 3. (4 points) The single-point method for solving non-linear equations sometimes diverges, how can you determine when this will occur? How can it be avoided? 4. (4 points) What is the key difference between boundary value problems and initial value problems? 5. (4 points) When would you use a spline rather than a polynomial for data interpolation? 6. (4 points) The Newton's method is considered the standard technique for solving systems of non- linear equations. List at least three potential disadvantages of this technique? 7.( 4 points) What are stiff ordinary differential equations? What is the simplest numerical technique for integrating such equations? Explain 8. (4 points) If you have to numerically integrate a arithmetic function, what technique is considered to be most efficient in terms of accuracy versus effort? Is this always so? Explain 9. (4 points) What are singular matrices? What are ill-conditioned matrices?

Explanation / Answer

1. Truncation error is the difference between a truncated value and the actual value. A truncated quantity is represented by a numeral with a fixed number of allowed digits, with any excess digits removed or chopped, hence they got their name the expression "truncated" meaning chopped. eg: 4.99768456 x 108 whenTruncated to two decimal places yields 2.99 x 108.

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