# cee_305_test_2_answers - Page 1 of 4 CEE 305 Civil&...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Page 1 of 4 CEE 305: Civil & Environmental Engineering Computation (Fall 2011}- Professor Duc T. Nguyen; 135 Kaufman (Ofﬁte #683-3761) ' Wed.I October 12, 2011; 3:002m — 4:15am; 10.12 BAL Closed Books/Notes; calculator is allowed _ Computer 8: internet are "NOT” allowed _ _ 1-page (both sides 85” x 11”} formulas/examples etc...is allowed Matrix Operations, Simultaneous Linear Eguations [SELCholesky Method. Fill—in-Terms - '5 Problem 01 I . , " . 1‘3"sz I:— —' } .rﬁq: nvr ' Given the following3 x 3 SLE [A1 * {x}={b}, where: ﬁg ('71) _' 3 4- ll = ‘ L! 2 —1 1 —3_ _ [A]: —1 4 —2 [b]: 9 y .3 2 -1 8 _ - 11 _ l _ l' i ‘ " I' ' tion method M1 0 a 5 - U N 6 Emma , _ 5 5mg aive auss /X- 0 0 C} ‘21-; Li a) Find the upper triangular matrix [U]?? b) Find the backward solution vector {x}?? 1" ’2 ._ [ - l 1 Problem 02 Given the foilowing 3 x 3 SLE [A] * {x} = {b}, where: _ 3 @ LC = 7 2 —1 .1 — 0 3|( .433“ [A]: —1 4 —2 [b]: 9 r; 2 -1 8 11 , D 0 Using L U Decomposition method, I 0;) v \ O O a) Find the upper triangular matrix [U]?? L: vol? 1 O l l b b) Find the lower triangular matrix [L1?? _ - 'g , +3 ' c) Find the forward solution vector {y}, from [L] -* {y} = {b}? a j ’ 1 .y d) Find the backward solution vector {x}, from [U] * {x} = {y}?? . _ [.414 O I'D Page20f4 : (AT - M95 D: 1 I . ] —o;7o’] my” 0 (To Sat-VIE a) i-LiiL-l, 0 2mm ProblemOS GiventhefollowinngSSLE[A]*{x}={b},where: ®_X "4‘4 4030.7 .lr‘fu‘i SF 2 —1 1 —3 [UL o from 0 [To SowE D) [A]= '1 4 “2 [b]: D o 2-”‘4’1 II is the given matrix [A] symmetric positive deﬁnite (SPD), explain your reasons?? #25 W 5- Me WIMAIJT ‘5 I b) Use the Cholesky method; find the upper triangular (or factorized) matrix IU]??¥ P05 "TV E- c) Find the forward solution vector {y}?? @2 '23 751'; #556 kW d) Find the backward solution vector {x}?? e} Find the product of [P]: [A]* {x} =?? 2 2x75: [P1 “3““ «“9 5f! ‘5 "1 - isﬁ r Problem '04 q Pl“: lo I” Given the following "symmetrica matrix: ' - O D a) Without any numerical calcUlation (just based on careful observation about the non-zero locations}, identify the "fill—in-term” |ocation(s} in the UPPER triangular matrix potions only, assuming ”Cholesky factorization method” is used?? Speciﬁcally, how many "upper triangular" ﬁll-in—terms wiil you have and where arethese ”ﬁll-in-terms” located? 2 FILL-1p T618115 @ M17, 4' ng b) Assuming METiS reordering algorithms have already been used to minimize the total number of fill-in- terms, and output from METiS reordering algorithms can be given as iPERM (new#) = {oldii}; .SuchasiPERM(1)={4} I 8 O O "D O iPERM(Z)={3} 4c , o o o ."9 o iPERM(3)={1} {A 1 '20 {go 3 ’D '9 iPERM(4) = {2} -2 . --> O 0 PERM-”=5” E; 3 lb Liz :50 Based on the given information/data,_ the original non-zero value for'A(2,4) = -5 (at the "old” location: row 2, column 4) will move to which ”new” iocation?? - A L bl , l ) Problem 05 toe rm 3cm - 3 . Page 3 of 4 05%) : 4N3 __ _,/ =00.30.15. X, - Y, - 4“ I 3 Given the following (n=4) data points: X; = 1.0 4.00 6.00 - vi: 3.0 4.00 8.00 - bl’f(x¢)*jm> .. finD’Jcl‘J , - . x?— '3‘: )ioax ; Where |=0, 1, 2 and (X0, X1, X2) = (1.0, 4.0, 6.0) x2 4‘: (Y0, Y1, Y2) = (3.0, 4.0, 8.0) 0 grid” , (“U-3 0-02.55 The Newton interpolation (2nd order polynomial) function can be expressed as: - [p '- L/ L; ., l 5 y=b0+b1(x—xo)+b2(xu-xo)(x—xl) ‘6" \$21. (Job? Find the unknown constants bu, b1, and b2?? L61; ) b): “0.337; )‘ 5'2“: lubleq’ Problem ’06 Given the following (n=3) data points: xi = 1.0 7 4.00 6.00 _ vi: 3.0 -4.00 8.00 thuul 5’) ((0-064—69) - (x~i‘)ix-V)(‘3) Where 1:0, 1, 2 and (Xe, X1, X2) = {1.0, 4.0, 6.0) ("(9 ’ | l C b , 4 ) (Yo. Y1, Y2) = (3.0, 74.0, 8.0) Using the Lagrange interpolation (2nd order polynomial), write the equation for y=f(x) that passes through the above 3 data points?? Regression... Problem 07 5 " H” E Given the following (n=4) data points: x, = 1.0 4.00 5.00 ' 6.00 5 Yi= 3.0 —4.00 8.00 -2.00 Where I=0, 1, 2 and (x0, x1, x2, x3) = (1.0, 4.0, 5.0, 6.0) Ll (b .7 8 ‘ 0,0 ‘3 (Y0, Y1, Y2, Y3) = (3.0, —4.0, 8.0, -2.0) __._ )5 . no '70 4 Uta 0“ The non-linear (2m1 order polynomial) function can be expressed as: . a £97 '75 LlDb 2:72; 2, _ 2 y—a0+a1x+a2x Setup (you do ”NOT” have to numerically solve) the appropriated equations 50 that the non-linear regression - "n coefﬁcuents a0, a1, and a; can be solved. . a0 : .2, 5-5 2; ﬁg *‘l-lC‘Hi “a = 0.!!8‘18 Page 4 of 4 Problem 08 [Al/~35: DATA Fag M Pia Woks Pace» am 1 Given the following (n=4) data points: '5 xi = 1.0 4.00 5.00 6.00 4 W Q " _ Yi=' 3.0 -4.00 8.00 72.00 _ .1 g _ . Ila '78 0; Where |=0, 1, 2 and (X0, X1, X2, X3) = (1.0, 4.0, 5.0, 6.0) _ ' (Y0. Y1. Y2, v3) = (3.0, -4.0, 8.0, —2.0) The linear (1St order polynomial) REGRESSION function can be expressed as: 053 y=.a0+a1x Find the linear REGRESSION coefficients a0 and a1??' 40 = 2. M78 6 at ‘ 'Déé'll ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern