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by: Moshe Swift III

NumericalAnalysisI MATH300

Moshe Swift III
GPA 3.63


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This 2 page Class Notes was uploaded by Moshe Swift III on Wednesday September 23, 2015. The Class Notes belongs to MATH300 at Drexel University taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/212296/math300-drexel-university in Mathematics (M) at Drexel University.

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Date Created: 09/23/15
Fall 2003 More Review Problems MATH 300 QOTEI Here are some more ICVICW pI39O ems t0 supp ementt e revrew pI39O ems Ol39t e quizzes l L 4 Lquot I N W 4 Lquot O gt1 Find the constants x0x1 and cl so that the quadrature formula A thirddegree polynomial Px satis es A3P0 6 and A2P0 l where APx Px l 7Px a lfPx a0 alx alzx2 a3x3 nd the coef cients a2 and 113 b Find A2P3 by using the fact that A2 110 alx 0 1 fxdx fx0 clfx1 has the highest 1 possible degree of precision Find an upper bound for the absolute error on the interval x0x1 for the Hermite polynomial interpolant H x for the function f x sinx where the points of interpolation are x0 10 and x1 12 Justify your answer It is NOT necessary to nd the interpolant A natural spline S on 02 is de ned as follows on 0 l Sx S0x l 2x7x339 on 12 Sx Sl x 71 8x 7 l Cxi l2 dx7 l3 Find the values ofthe parameters c and d Consider the following numerical approximation for the second derivative of f x at x 0 fr 0 L fh 7 2f0 fh lt gt i 2 h Find the order of the error of this approm ation in the form of a dominant term and the order of the higher order terms by using a taylor series expansion Your answer should have the form const h 0 if MULTIPLE CHOICE AND TRUEFALSE QUESTIONS Suppose that L Lh k1h2 k2h4 is an approximation to the value L If Richardson s extrapolation is applied once we obtain the formula where L0 h Lh2 0LLh2 7Lh where a0Ll3 boc115 cm 131 1 Consider the integral sinx dx Among the three choices below which is the largest step size h which will guarentee that the composite trapezodial approximation will have absolute error less than 0001 a h 005 b h 010 c h 015 Consider the exponential function f x e on 0 05 Consider the polynomial interpolant 75 x to f x at the points x0 x1 xz 02x3 03x4 04 and x5 05 Then the Lagrange estimate ofthe absolute error between f x and the interpolant 75 x is bounded above by a 104 b 105 10 1 Consider the integral cos2x dx Among the three choices below which is the largest step size h which will 1 guarentee that the composite Simpson approximation will have absolute error less than 0001 a h 030 b h 035 c h 040 b Consider a twopoint quadrature rule for an integral on 11 fx dx cofx0 clfx1 Then the maximal possible degree of precision for such a rule is 801 b 3 c 4 b Consider a threepoint quadrature rule for an integral on 11 fx dx cofx0 clfx1 czfx2 Which of the following a 4 b 5 There is a fthdegree polynomial px such that ll pxqx dx 0 for any polynomial of degree 4 or less a TRUE b FALSE degrees of precision is impossible for such a rule c 6 8 Let fx be a polynomial with lf xl S 05 for all x E 70505 We consider the method of successive substitution to approximate its xed point with the initial starting value x0 01 It is possible for the order of convergence to be two a TRUE b FALSE 9 Let fx be apolynomial with if 2 2 for allx E 70505 Then it is impossible forfto have a xed point in 705 05 a TRUE b FALSE


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