Numerical Methods in Engineering with Python Phần 7 pdf

... LU = ⎡ ⎢ ⎣ 200 12 0 1 11 ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ 4 − 31 04−3 002 ⎤ ⎥ ⎦ P1: PHB CUUS884-Kiusalaas CUUS884- 01 978 0 5 21 1 913 2 6 December 16 , 2009 15 :4 3 1. 2 Core Python for k in range(n -1, -1, -1) : b[k] = (b[k] ... ones((2,2)) [[ 1. 1. ] [ 1. 1. ]] P1: PHB CUUS884-Kiusalaas CUUS884-FM 978 0 5 21 1 913 2 6 December 16 , 2009 15 :4 ii P1: PHB CUUS884-Kiusalaas CUUS884-02 978...

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... in Eq. (2. 16) we obtain ⎡ ⎢ ⎣ 4 22 22 −4 2 −411 ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ L 2 11 L 11 L 21 L 11 L 31 L 11 L 21 L 2 21 + L 2 22 L 21 L 31 + L 22 L 32 L 11 L 31 L 21 L 31 + L 22 L 32 L 2 31 + L 2 32 + L 2 33 ⎤ ⎥ ⎦ Equating ... L 2 33 ⎤ ⎥ ⎦ Equating the elements in the lower (or upper) triangular portions yields L 11 = √ 4 = 2 L 21 = 2/ L 11 = 2/ 2 =−1 L 31 = 2/...

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... 10 ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ 1.1 23 32 4. 236 92 −1.848 28 ⎤ ⎥ ⎦ β 0 =− r T 1 As 0 s T 0 As 0 =− 1.1 23 32(54) + 4. 236 92(−26) −1.848 28 (34 ) 12(54) +(−1)(−26) +5 (34 ) = 0. 133 107 s 1 = r 1 + β 0 s 0 = ⎡ ⎢ ⎣ 1.1 23 32 4. 236 92 −1.848 ... (pivoting is recommended). Run the program with n = 2, 3, and 4 and comment on the results. 20.  3m /s 3 2 m /s 3 4 m /s 3 2 m /s 3 4 m /s 3 2 m /s...

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... range(m+1): for j in range(m+1): a[i,j] = s[i+j] return gaussPivot(a,b) P1: PHB CUUS8 84- Kiusalaas CUUS8 84- 04 978 0 521 19132 6 December 16, 2009 15 :4 149 4. 4 Methods Based on Linear Interpolation Second ... the denominator in Eq. (3.15) are zero, so that σ is indeterminate. Fitting a Straight Line Fitting a straight line f (x) = a +bx (3.16) to data is also known as linear reg...

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... the root-finding methods in Chapter 2. This was done with α = 0 ◦ ,5 ◦ ,10 ◦ , ,30 ◦ ,the results being α (deg) 0 5 10 15 20 25 30 β (rad) 1. 659 5 1 .54 34 1.4186 1.29 25 1.1712 1. 058 5 0. 956 1 If link ABrotates ... 0. 05 0.10 0. 15 0.20 0. 25 F (N) 0 37 71 104 134 161 x (m) 0.30 0. 35 0.40 0. 45 0 .50 F (N) 1 85 207 2 25 239 250 P1: PHB CUUS884-Kiusalaas CUUS884- 05...

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... 0.3 86 875 0.314 020 0.245 317 0.5 56 165 0.190 435 0.538 65 7 0.142 009 0.848 982 (−1)0.392 255 0.7 56 9 16 (−1)0.554 5 46 0.922 66 9 (−1)0.101 69 0 Table 6. 6 Multiply numbers by 10 k ,wherek is given in ... prints every nth step. freq = 0 prints initial and final values only. ’’’ def printSoln(X,Y,freq): def printHead(n): print ’’\n x ’’, for i in range (n): print ’’ y[’’,i,’’...

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... 15:4 292 Two-Point Boundary Value Problems  linInterp Here is the algorithm we use for linear interpolation: ## module linInterp ’’’ root = linInterp(f,x1,x2). Finds the zero of the linear function ... 1.3848e+000 4.0000e-001 5.4 170 e-001 1. 074 3e+000 6.0000e-001 7. 2187e-001 7. 3287e-001 8.0000e-001 8.3944e-001 4. 575 2e-001 1.0000e+000 9.1082e-001 2 .70 13e-001 1.2000e+000 9.5227e-001...

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... 9.7152e-001 7.0 683 e-001 -1 .86 66e-001 -4.4722e-001 -2 .88 96e-001 9.7627e-001 9 .88 85e-001 -3.2061e-001 -4 .89 68e-001 -1.1144e-002 9. 984 8e-001 1.0000e+000 -3.2607e-001 -4 .89 75e-001 -6.7428e-011 1.0000e+000 x 0.00 ... = ( −0.535 18 )( 0 .88 1 68 ) =−0.471 86 τ = s 1 +c = −0.47 186 1 +0 .88 1 68 =−0.250 77 We obtain the changes in the transformation matrix P from Eqs. (9.20). R...

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... 0.26726603 0.7 291 0002 0.505 791 64] [-0.74142854 0.41 391 448 -0.31882387] [-0.05017271 -0.4 298 6 39 0.52077788] [ 0. 594 91453 0.0 695 5611 -0.60 290 543] [-0.1 497 0633 -0.32782151 -0.0884 398 5]] PROBLEM SET 9. 2 1. ... PHB CUUS884-Kiusalaas CUUS884- 09 978 0 521 191 32 6 December 16, 20 09 15:4 357 9. 4 Householder Reduction to Tridiagonal Form QA  Q = ⎡ ⎢ ⎣ 10.642 −0.1388 9. 1 2...

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... linear regression, 128–129 polynomial interpolation, 99 107 Lagrange’s method, 99 101 limits of, 106 107 Neville’s method, 104 106 Newton’s method, 101 103 rational function interpolation, 110 112 interval ... 244–246 Input/output printing, 12–13 reading, 13–14 writing, 14 integration order, 229 interpolation, derivatives by, 185–186 cubic spline interpolant, 186 polynomial interpolan...

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... political parties; State governments; 20 | Chapter 1: Language Processing and Python 3 .10 Summary 12 1 3 .11 Further Reading 12 2 3 .12 Exercises 12 3 4. Writing Structured Programs . . . . . . . . ... ix 1. Language Processing and Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 .1 Computing with Language: Texts and Words...

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... 4 21 26 austen-emma.txt 4 23 16 austen-persuasion.txt 4 24 22 austen-sense.txt 4 33 79 bible-kjv.txt 4 18 5 blake-poems.txt 4 17 14 bryant-stories.txt 4 17 12 burgess-busterbrown.txt 4 16 12 ... (McEnery, 20 06), (Meyer, 20 02) , (Sampson & McCarthy, 20 05), and (Scott & Tribble, 20 06). Further readings in quan- titative data analysis in linguistics are: (Baayen, 20 08),...

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... 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% –up 49.9% 4. 46% 4. 46% 4. 46% 4. 46% 4. 46% 4. 46% 4. 46% 4. 46% 4. 46% In particular, the distribution is consistent with what we know: if we add up the prob- abilities ... (e.g., as part of a language processing system), then we can use the model to make predictions about new data without worrying about the details of underlying causal relationshi...

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... serve as a model of psycholinguistic processing, helping to explain the difficulties that humans have with processing certain syntactic constructions. Many natural language applica- tions involve ... constraints that govern sentences. We need a way to deal with the ambiguity that natural language is famous for. We also need to be able to cope with the fact that there are an u...

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