Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Numerical Methods:
LU decomposition for systems of linear equations
Numerical solutions of non-linear algebraic equations by Secant, Bisection and Newton-Raphson Methods
Numerical integration by trapezoidal and Simpson’s rules
Recent questions tagged numerical-methods
3
votes
1
answer
31
GATE IT 2004 | Question: 38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula?88(1/3)8(2/3)9
Ishrat Jahan
3.7k
views
Ishrat Jahan
asked
Nov 2, 2014
Numerical Methods
gateit-2004
numerical-methods
lagranges-interpolation
normal
out-of-syllabus-now
non-gate
+
–
1
votes
1
answer
32
GATE IT 2006 | Question: 77
$x + y/2 = 9$ $3x + y = 10$ What can be said about the Gauss-Siedel iterative method for solving the above set of linear equations? it will converge It will diverse It will neither converge nor diverse It is not applicable
$x + y/2 = 9$$3x + y = 10$What can be said about the Gauss-Siedel iterative method for solving the above set of linear equations?it will convergeIt will diverseIt will...
Ishrat Jahan
1.7k
views
Ishrat Jahan
asked
Nov 1, 2014
Linear Algebra
gateit-2006
linear-algebra
normal
numerical-methods
non-gate
+
–
1
votes
1
answer
33
GATE IT 2006 | Question: 76
x + y/2 = 9 3x + y = 10 The value of the Frobenius norm for the above system of equations is $0.5$ $0.75$ $1.5$ $2.0$
x + y/2 = 93x + y = 10The value of the Frobenius norm for the above system of equations is$0.5$$0.75$$1.5$$2.0$
Ishrat Jahan
1.5k
views
Ishrat Jahan
asked
Nov 1, 2014
Linear Algebra
gateit-2006
linear-algebra
normal
numerical-methods
non-gate
+
–
8
votes
3
answers
34
GATE IT 2006 | Question: 28
The following definite integral evaluates to $\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$
The following definite integral evaluates to$$\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$$$\frac{1}{2}$$\pi \sqrt{10}$$\sqrt{10}$$\pi$
Ishrat Jahan
5.1k
views
Ishrat Jahan
asked
Oct 31, 2014
Numerical Methods
gateit-2006
numerical-methods
normal
non-gate
+
–
0
votes
0
answers
35
GATE IT 2006 | Question: 27
Match the following iterative methods for solving algebraic equations and their orders of convergence. Method Order of Convergence 1. Bisection P. 2 or more 2. Newton-Raphson Q. 1.62 3. Secant R. 1 4. Regula falsi S. 1 bit per iteration I-R, II-S, III-P, IV-Q I-S, II-R, III-Q, IV-P I-S, II-Q, III-R, IV-P I-S, II-P, III-Q, IV-R
Match the following iterative methods for solving algebraic equations and their orders of convergence. Method Order of Convergence1.BisectionP.2 or more2.Newton-RaphsonQ....
Ishrat Jahan
1.5k
views
Ishrat Jahan
asked
Oct 31, 2014
Numerical Methods
gateit-2006
numerical-methods
normal
out-of-gate-syllabus
+
–
4
votes
1
answer
36
GATE IT 2007 | Question: 77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c > 0$. For which of the following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the ... $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c 0$.For which of the f...
Ishrat Jahan
1.5k
views
Ishrat Jahan
asked
Oct 30, 2014
Numerical Methods
gateit-2007
numerical-methods
normal
non-gate
+
–
0
votes
1
answer
37
GATE IT 2007 | Question: 22
The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$. Consider the following values for the step size h. 10-2 10-3 10-4 10-5 For which of these values of the step size h, is the computed value guaranteed to be correct ... that there are no round-off errors in the computation. iv only iii and iv only ii, iii and iv only i, ii, iii and iv
The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$. Consider the following values for the step size h.10-210-310-410-5For which of th...
Ishrat Jahan
1.5k
views
Ishrat Jahan
asked
Oct 29, 2014
Numerical Methods
gateit-2007
numerical-methods
trapezoidal-rule
normal
out-of-syllabus-now
+
–
0
votes
1
answer
38
GATE IT 2008 | Question: 30
Consider the function f(x) = x2 - 2x - 1. Suppose an execution of the Newton-Raphson method to find a zero of f(x) starts with an approximation x0 = 2 of x. What is the value of x2, the approximation of x that algorithm produces after two iterations, rounded to three decimal places? 2.417 2.419 2.423 2.425
Consider the function f(x) = x2 - 2x - 1. Suppose an execution of the Newton-Raphson method to find a zero of f(x) starts with an approximation x0 = 2 of x. What is the v...
Ishrat Jahan
1.1k
views
Ishrat Jahan
asked
Oct 28, 2014
IS&Software Engineering
gateit-2008
numerical-methods
newton-raphson
normal
+
–
4
votes
2
answers
39
GATE CSE 1996 | Question: 2.5
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c 0$ is$x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$$x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$$x_{...
Kathleen
1.8k
views
Kathleen
asked
Oct 9, 2014
Numerical Methods
gate1996
numerical-methods
newton-raphson
normal
out-of-syllabus-now
+
–
0
votes
3
answers
40
GATE CSE 1995 | Question: 2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is$x_{k+1} = 3(x_k+b)/2x_k$$x_{k+1} = (x_{k}^2+b)/2x_k$$x_{k+1...
Kathleen
2.5k
views
Kathleen
asked
Oct 8, 2014
Numerical Methods
gate1995
numerical-methods
newton-raphson
normal
out-of-gate-syllabus
+
–
0
votes
3
answers
41
GATE CSE 1994 | Question: 3.4
Match the following items (i) Newton-Raphson (a) Integration (ii) Runge-Kutta (b) Root finding (iii) Gauss-Seidel (c) Ordinary Differential Equations (iv) Simpson's Rule (d) Solution of Systems of Linear Equations
Match the following items(i) Newton-Raphson(a) Integration(ii) Runge-Kutta(b) Root finding(iii) Gauss-Seidel(c) Ordinary Differential Equations(iv) Simpson's Rule(d) Solu...
Kathleen
11.8k
views
Kathleen
asked
Oct 4, 2014
Numerical Methods
gate1994
numerical-methods
easy
out-of-gate-syllabus
+
–
0
votes
0
answers
42
GATE CSE 1994 | Question: 1.3
Backward Euler method for solving the differential equation $\frac{dy}{dx}=f(x, y)$ is specified by, (choose one of the following). $y_{n+1}=y_n+hf(x_n, y_n)$ $y_{n+1}=y_n+hf(x_{n+1}, y_{n+1})$ $y_{n+1}=y_{n-1}+2hf(x_n, y_n)$ $y_{n+1}= (1+h)f(x_{n+1}, y_{n+1})$
Backward Euler method for solving the differential equation $\frac{dy}{dx}=f(x, y)$ is specified by, (choose one of the following).$y_{n+1}=y_n+hf(x_n, y_n)$$y_{n+1}=y_n+...
Kathleen
1.1k
views
Kathleen
asked
Oct 4, 2014
Numerical Methods
gate1994
numerical-methods
backward-euler-method
out-of-gate-syllabus
+
–
0
votes
1
answer
43
GATE CSE 1997 | Question: 4.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the widt...
Kathleen
1.5k
views
Kathleen
asked
Sep 29, 2014
Numerical Methods
gate1997
numerical-methods
trapezoidal-rule
normal
+
–
0
votes
0
answers
44
GATE CSE 1997 | Question: 4.3
Using the forward Euler method to solve $y’'(t) = f(t), y’(0)=0$ with a step size of $h$, we obtain the following values of $y$ in the first four iterations: $0, hf (0), h(f(0) + f(h)) \text{ and }h(f(0) - f(h) + f(2h))$ $0, 0, h^2f(0)\text{ and } 2h^2 f(0) + f(h)$ $0, 0, h^2f(0) \text{ and } 3h^2f(0)$ $0, 0, hf(0) + h^2f(0) \text{ and }hf (0) + h^2f(0) + hf(h)$
Using the forward Euler method to solve $y’'(t) = f(t), y’(0)=0$ with a step size of $h$, we obtain the following values of $y$ in the first four iterations:$0, hf (0...
Kathleen
674
views
Kathleen
asked
Sep 29, 2014
Numerical Methods
gate1997
numerical-methods
non-gate
out-of-gate-syllabus
+
–
3
votes
2
answers
45
GATE CSE 1997 | Question: 1.2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations will converge to -1 converge to $\sqrt{2}$ converge to $\sqrt{-2}$ not converge
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations willconverge to -1converge to $\sqrt{2...
Kathleen
12.1k
views
Kathleen
asked
Sep 29, 2014
Numerical Methods
gate1997
numerical-methods
newton-raphson
normal
non-gate
out-of-gate-syllabus
+
–
5
votes
1
answer
46
GATE CSE 2014 Set 3 | Question: 46
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/are TRUE? The value of $K$ obtained using the trapezoidal rule is always ... ;s rule is always equal to the exact value of the definite integral. I only II only Both I and II Neither I nor II
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/ar...
go_editor
3.5k
views
go_editor
asked
Sep 28, 2014
Numerical Methods
gatecse-2014-set3
numerical-methods
trapezoidal-rule
simpsons-rule
normal
+
–
7
votes
1
answer
47
GATE CSE 2014 Set 2 | Question: 46
In the Newton-Raphson method, an initial guess of $x_0= 2 $ is made and the sequence $x_0,x_1,x_2\:\dots$ is obtained for the function $0.75x^3-2x^2-2x+4=0$ Consider the statements $x_3\:=\:0$ The method converges to a solution in a finite number of iterations. Which of the following is TRUE? Only I Only II Both I and II Neither I nor II
In the Newton-Raphson method, an initial guess of $x_0= 2 $ is made and the sequence $x_0,x_1,x_2\:\dots$ is obtained for the function $$0.75x^3-2x^2-2x+4=0$$Consider the...
go_editor
2.2k
views
go_editor
asked
Sep 28, 2014
Numerical Methods
gatecse-2014-set2
numerical-methods
newton-raphson
normal
non-gate
+
–
1
votes
1
answer
48
GATE CSE 1998 | Question: 1.3
Which of the following statements applies to the bisection method used for finding roots of functions: converges within a few iterations guaranteed to work for all continuous functions is faster than the Newton-Raphson method requires that there be no error in determining the sign of the function
Which of the following statements applies to the bisection method used for finding roots of functions:converges within a few iterationsguaranteed to work for all continuo...
Kathleen
22.4k
views
Kathleen
asked
Sep 25, 2014
Numerical Methods
gate1998
numerical-methods
bisection-method
easy
out-of-gate-syllabus
+
–
7
votes
1
answer
49
GATE CSE 2012 | Question: 28
The bisection method is applied to compute a zero of the function $f(x) =x ^{4} – x ^{3} – x ^{2} – 4$ in the interval [1,9]. The method converges to a solution after ––––– iterations. (A) 1 (B) 3 (C) 5 (D) 7
The bisection method is applied to compute a zero of the function $f(x) =x ^{4} – x ^{3} – x ^{2} – 4$ in the interval [1,9]. The method converges to a solution aft...
Arjun
4.0k
views
Arjun
asked
Sep 25, 2014
Numerical Methods
gatecse-2012
numerical-methods
bisection-method
+
–
3
votes
2
answers
50
GATE CSE 2013 | Question: 23
Function $f$ is known at the following points: $x$ 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 $f(x)$ 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00 The value of $\int_{0}^{3} f(x) \text{d}x$ computed using the trapezoidal rule is (A) 8.983 (B) 9.003 (C) 9.017 (D) 9.045
Function $f$ is known at the following points:$x$00.30.60.91.21.51.82.12.42.73.0$f(x)$00.090.360.811.442.253.244.415.767.299.00The value of $\int_{0}^{3} f(x) \text{d}x$ ...
Arjun
3.5k
views
Arjun
asked
Sep 24, 2014
Numerical Methods
gatecse-2013
numerical-methods
trapezoidal-rule
non-gate
+
–
6
votes
2
answers
51
GATE CSE 1999 | Question: 1.23
The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$ is the derivative of $f$. The method converges always only if $f$ is a polynomial only if $f(x_o) <0$ none of the above
The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$ is the derivative of $f$. The metho...
Kathleen
3.0k
views
Kathleen
asked
Sep 23, 2014
Numerical Methods
gate1999
numerical-methods
newton-raphson
normal
out-of-syllabus-now
+
–
1
votes
0
answers
52
GATE CSE 2007 | Question: 28
Consider the series $x_{n+1} = \frac{x_n}{2}+\frac{9}{8x_n},x_0 = 0.5$ obtained from the Newton-Raphson method. The series converges to 1.5 $\sqrt{2}$ 1.6 1.4
Consider the series $x_{n+1} = \frac{x_n}{2}+\frac{9}{8x_n},x_0 = 0.5$ obtained from the Newton-Raphson method. The series converges to1.5$\sqrt{2}$1.61.4
Kathleen
1.0k
views
Kathleen
asked
Sep 21, 2014
IS&Software Engineering
gatecse-2007
numerical-methods
newton-raphson
normal
out-of-syllabus-now
+
–
3
votes
1
answer
53
GATE CSE 2010 | Question: 2
Newton-Raphson method is used to compute a root of the equation $x^2 - 13 = 0$ with 3.5 as the initial value. The approximation after one iteration is 3.575 3.676 3.667 3.607
Newton-Raphson method is used to compute a root of the equation $x^2 - 13 = 0$ with 3.5 as the initial value. The approximation after one iteration is3.5753.6763.6673.607...
gatecse
6.2k
views
gatecse
asked
Sep 21, 2014
Numerical Methods
gatecse-2010
numerical-methods
newton-raphson
easy
non-gate
+
–
0
votes
0
answers
54
GATE CSE 2003 | Question: 42
A piecewise linear function $f(x)$ is plotted using thick solid lines in the figure below (the plot is drawn to scale). If we use the Newton-Raphson method to find the roots of \(f(x)=0\) using \(x_0, x_1,\) and \(x_2\) respectively as initial guesses, the ... .6 respectively 0.6, 0.6, and 1.3 respectively 1.3, 1.3, and 0.6 respectively 1.3, 0.6, and 1.3 respectively
A piecewise linear function $f(x)$ is plotted using thick solid lines in the figure below (the plot is drawn to scale).If we use the Newton-Raphson method to find the roo...
Kathleen
1.4k
views
Kathleen
asked
Sep 17, 2014
Numerical Methods
gatecse-2003
numerical-methods
newton-raphson
normal
out-of-syllabus-now
+
–
0
votes
1
answer
55
GATE CSE 2002 | Question: 2.15
The Newton-Raphson iteration $X_{n+1} = (\frac{X_n}{2}) + \frac{3}{(2X_n)}$ can be used to solve the equation $X^2 =3$ $X^3 =3$ $X^2 =2$ $X^3 =2$
The Newton-Raphson iteration $X_{n+1} = (\frac{X_n}{2}) + \frac{3}{(2X_n)}$ can be used to solve the equation$X^2 =3$$X^3 =3$$X^2 =2$$X^3 =2$
Kathleen
840
views
Kathleen
asked
Sep 15, 2014
Numerical Methods
gatecse-2002
numerical-methods
normal
non-gate
+
–
1
votes
1
answer
56
GATE CSE 2002 | Question: 1.2
The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree 0 but not 1 1 but not 0 0 or 1 2
The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree0 but not 11 but not 00 or 12
Kathleen
4.8k
views
Kathleen
asked
Sep 15, 2014
Numerical Methods
gatecse-2002
numerical-methods
trapezoidal-rule
easy
non-gate
+
–
30
votes
3
answers
57
GATE CSE 2006 | Question: 1, ISRO2009-57
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is: 3 4 6 9
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input ...
gatecse
11.4k
views
gatecse
asked
Sep 15, 2014
Numerical Methods
gatecse-2006
numerical-methods
normal
isro2009
+
–
5
votes
2
answers
58
GATE CSE 2000 | Question: 2.1
X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true? k must be 1 k must be 0 k can take any value between 0 and 1 None of the above
X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X a...
Kathleen
1.9k
views
Kathleen
asked
Sep 14, 2014
Numerical Methods
gatecse-2000
numerical-methods
normal
non-gate
out-of-gate-syllabus
+
–
0
votes
0
answers
59
GATE CSE 1993 | Question: 02.4
Kathleen
381
views
Kathleen
asked
Sep 13, 2014
Numerical Methods
gate1993
numerical-methods
runga-kutta-method
out-of-gate-syllabus
fill-in-the-blanks
+
–
1
votes
1
answer
60
GATE CSE 1993 | Question: 01.3
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree $1$ $2$ $3$ $4$
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree$1$$2$$3$$4$
Kathleen
5.2k
views
Kathleen
asked
Sep 13, 2014
Numerical Methods
gate1993
numerical-methods
simpsons-rule
easy
out-of-gate-syllabus
multiple-selects
+
–
Page:
« prev
1
2
3
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register