Question

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Problem 15. Mark each of the following statements as true or false: but 1. A three-term recurrence relation for orthogonal polynomials is theoretically useful rei not practical for numerical calculation. 2. Standard double-precision floating point arithmetic has a precision of about 10-16 3. Spline interpolation is based on a mathematical model of an old technique of making curves by stringing thin pieces of wood between nodes. 4. The composite trapezoid rule is particularly effective for integrating periodic func- tions 5. A typical laptop computer runs about 1000 floating point operations per second. 6. Monte Carlo integration is most useful for low-dimensional problems. 7. Euler's method has local truncation error o (ir) 8. Simpson's Rule is derived by exact integration of a quadratic interpolating polynomial, but also integrates cubics exactly. 9. If an ODE integration method has local truncation error O (h), the global truncation error is O (h6). 10. Tchebyshev polynomials are closely related to trigonometric functions.

Answer 1

2) True S False b〉 false g〉, a) balse Tru e