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Class: AOE 2074 - Computational Methods; Subject: Aerospace and Ocean Engineerin; University: Virginia Polytechnic Institute And State University; Term: Fall 2010;
Typology: Quizzes
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DEFINITION 2
DEFINITION 3 !)script 2) function TERM 4
DEFINITION 4 outvar=funcname(arglist) TERM 5
DEFINITION 5 1)listed 1st in m file 2)function name same as file name
1)only accessible by primary function or sub functions within the same m file. 2) Not accesible by command window TERM 7
DEFINITION 7 simple one line functions created without need for a seperate m file TERM 8
DEFINITION 8 functions that operate on other functions -passed to it as input arguments TERM 9
DEFINITION 9 -ends after certain number of iterations - index=start:step:finish TERM 10
DEFINITION 10 ends based on a condition being met
-fixed point iteration -Newt-raphson -CAN DIVERGE -Require only single starting guess -IF converge, converge faster than bracketing methods TERM 17
DEFINITION 17 -Mostly widely used for finding roots -Start with inital guess - calculate tangent at f(guess) -intersection of tangent with x- axis becomes next guess -may have problems with 1) multiple roots, 2) slow convergence or divergence TERM 18
DEFINITION 18 Pro=quadratic convergence Con=sometimes poor or slow convergence TERM 19
DEFINITION 19 How closely a computed value agress with the true value TERM 20
DEFINITION 20 How closely individual measurements agree with each other
difference between true value and its approximate TERM 22
DEFINITION 22 absolute difference between true value and the approximate TERM 23
DEFINITION 23 (present-previous)/present TERM 24
DEFINITION 24 (present-previous)/present * 100% TERM 25
DEFINITION 25 -usually sign of error ignored -computations usually computed until ea
---Blunders- errors caused by computer/human imperfections ----Model Errors= errors resulting from incorrect mathematical models ------Data uncertainty=errors resulting from the accuracy/precision of data TERM 32
DEFINITION 32 Process of creating something as efficient as possible TERM 33
DEFINITION 33 represents very best solution TERM 34
DEFINITION 34 is better than its immediate neighbor ----want to find global optimum though TERM 35
DEFINITION 35
uses 3 points to estimate optimum location TERM 37
DEFINITION 37 -matlab function combines parablolic interpolation and golden ratio ---fminbnd(func,x1,x2) TERM 38
DEFINITION 38 matlab code to determine minimum of multidimensional function -------fminshearch(function,x0) TERM 39
DEFINITION 39 Systems of Linear Algebraic Equations TERM 40
DEFINITION 40 More equations than unknowns
DEFINITION 47 --occur comonly in engineering --special techniques to solve TERM 48
DEFINITION 48 -Most popular way to solve symmetric systems ---Symmetric system decomposed into A=U(transpose) *U --matlab=== U=chol(A) TERM 49
DEFINITION 49 examines most efficient way to solve a system -----Banded Solvers -----Back or forward substitutions if triangular matrix - ----Cholesky Factorization if symmetric -----Gauss+partial pivoting if square TERM 50
DEFINITION 50 ---Scale matrix A so largest element in each row is 1 and invert. IF A inverse has larger elements its ill ---Multiply A by A(invert), if don't real close to identity its illl ----invert A to see if close to A, if not its ill
Single Number utilized to indicate if ill conditioned TERM 52
DEFINITION 52 real-valued function ---provides measure of length of multi component mathematical entities TERM 53
DEFINITION 53 -solves each equation in a system for a particular variable --- Then uses that value later on in the equation TERM 54
DEFINITION 54 ---If diaganoly dominant a system will converge TERM 55
DEFINITION 55 Enhancement of convergence utilizing relaxation
calculates standard deviation of s TERM 62
DEFINITION 62 Minimize the sum of the squares of the residuals TERM 63
DEFINITION 63 p=polyfit(x,y, n) ---n=order of polynomial to fit TERM 64
DEFINITION 64 ---computes coefficients ----y=polyval(p,x) p=matrix from polyfit TERM 65
DEFINITION 65 -----ill-conditioned ----due to exponential growth, large round- off errors
---Linear Interpolation formula uses similar triangles ---- smaller the interval the better the approximate TERM 67
DEFINITION 67 --shifts values to express interpolating polynomial TERM 68
DEFINITION 68 -finding x where f(x) is a certain value TERM 69
DEFINITION 69 The process of estimating a value f(x) that lies outside the range of the base points --extends curve beyond know region TERM 70
DEFINITION 70 Higher-order polynomials can lead to ill conditioning and may introduce oscillations where there shouldnt be
assume 1st derivative at 1st and last knots known TERM 77
DEFINITION 77 forces continuity of 3rd derivative TERM 78
DEFINITION 78 yy=spline(x, y, xx) -----performs cubic spline interpolation ----- uses 'not a knot' condition by default TERM 79
DEFINITION 79 yi=interpl1(x,y,xi,'method') ---x&y are original data sets ----- xi= contains points at which want to interpolate ----- method=sting containing desired method TERM 80
DEFINITION 80 nearest=nearest neighbor interpolation ------linear=connects points with straight line(default) ------spline=not-a-knot cubic interpolation ------pchip=piecewise hermite interpolation
Use 2 estimates of an integral to compute a 3rd more accurate approximate TERM 82
DEFINITION 82 class of techniques for evaluating area under a straight line -- --choose line that minimizes error TERM 83
DEFINITION 83 optimizes estimates to integrals for functions over intervals from -1 to 1 ------other intervals require a change to -1 to 1 TERM 84
DEFINITION 84 disadvantage of equal spacing ----functions with regions of abrupt change need small step over entire domain to achieve a certain accuracy TERM 85
DEFINITION 85 small steps are taken in regions of sharp variations ------- larger steps where function changes gradually
diff(x) returns the difference between adjacent elements in x
fx=gradiant (f,h) determines derivative of data in f at each point TERM 92
DEFINITION 92 contour(x,y,z) generates contour plot TERM 93
DEFINITION 93 quiver(x,y,fx,fy) ___generates vector field
