Numerical Methods Test 1

(T/F) When it converges, the newton raphson method does so very quickly

True

(T/F) For the third iteration in the newton rhapson method you will use the estimated root location from the first iteration as the NEW initial point

False

_______ Can separate both array elements and multiple commands

, (comma)

(T/F) MATLAB's built in f-zero function uses a combination of a search algorithm, bisection, and inverse quadratic interpolation

True

(T/F) One disadvantage of the newton rhapson method is that it requires the user to analytically find the derivatives of the function

True

(T/F) The bisection method is a bracketing method

True

(T/F) The function name must be the same as the filename

True

(T/F) The secant method requires two initial estimates of x, but does not require an analytical expression of the derivative

True

What is the first step if you are asked to find all real roots of a function?

GRAPH THE FUNCTION

(T/F) For the bisection algorithm, the number of iterations required to attain a particular error can be calculated in advance

TRUE

The false position method is based on the false assumption that the function can be approximated by a(n) _________________________

straight line

When creating spacing in an array how should it be written. make array x go from 0-10 in increments of 0.1

x = 0:0.1:10

what is the percent relative error formula

(current guess - previous guess)/current guess

What would a single input in a function look like? (IDK its a func question)

(telescopeData)

Out of the following which root-finding methods require only one initial guess? -False position -Secant -Newton Rhapson -Modified Secant -Bisection

-Newton Rhapson -Modified Secant

How many inputs are in the following function? [a,b] = quiz1(c,d,e,f,g)

5

suppresses outputs to the command window and separates rows in arrays

; (semicolon)

Which 3 commands will calculate the inverse of matrix "A"

A^(-1) A^-1 inv(A)

(T/F) The secant method requires two initial estimates, but they are NOT required to bracket the root

True

(T/F) All mathematical problems have a closed-form solution (i.e. the can be solved for a variable without having to make guesses.)

False

(T/F) For the bisection algorithm, the number of iterations required to attain a particular error cannot be calculated in advance

False

(T/F) If the function values of a bracket have the same sign, there are guaranteed to be no roots in the brackets

False

(T/F) Inflection points and local max and mins greatly increase the speed at which the newton rhapson method converges

False

(T/F) Newton-Rahpson is not an iterative method

False

(T/F) The incremental search method is typically very fast, even when employing a high degree of precision.

False

(T/F) The main Advantage of the newton rhapson method is that it always converges

False

(T/F) The main advantage of newton rahpson is that it always converges

False

(T/F) The main advantage of the secant method is that it is guaranteed to converge

False

(T/F) The main disadvantage of the false position method is that it can diverge

False

(T/F) The main disadvantage of the modified secant method is that it does not require specifying a value for DeltaX

False

The secant method is similar to the newton rhapson method, does this mean it requires the derivative of the function to be known?

No, It does not require the derivative of the function to be known

(T/F) Anonymous functions need to be defined before being used

True

(T/F) Another name for the false position method is the regula-falsi method

True

(T/F) Bracketing methods ALWAYS require two initial estimates

True

(T/F) Bracketing methods always converge but usually do so more slowly than open methods

True

(T/F) For the fourth iteration in the newton rhapson method, you will use the estimated root location from the third iteration as the new initial point

True

(T/F) In mathematics, a root (a zero) of a function f(x) is a value for x that produces f(x) = 0

True

(T/F) In the newton rhapson method, the new estimate at Xi+1, is the intersection of the tangent line and the X-axis

True

(T/F) Incsearch can be used to find the number of roots of a function between a specific lower and upper bound

True

(T/F) MATLAB can solve problems without closed-form solutions

True

(T/F) Tangent points in a function cause an opposite valued bracket to contain an even number of roots

True

(T/F) The false position algorithm is identical to the bisection algorithm, except for the calculations for the estimated root locations

True

(T/F) The main DISadvantage of the newton rhapson method is that it may not converge

True

What kind of method are bisection and false position?

bracketing

Which line will give us the cross product of a and b? -cross(a,b) -cross[a,b] -cross(a*b) -cross[a*b]

cross(a,b)

Which is the correct command for factorial of "m" -factorial[m] -Factorial[m] -factorial(m) -factorial(M)

factorial(m)

create function header with no error using quiz1_question4.m

function[d,e] = quiz1_qquestion4(a,b,c)

suppose you are given: [a,b] = mae284(p,q,r,s) if the user doesnt specify the input for "s" how would you write the nargin line to replace "s" with the default value 100

if nargin <4, s = 100; end