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Numerical Analysis and Simulation
The study of algorithms for problems related to continuous mathematics
818 Questions
54 , or am i missing a joke here? In base 13 six times nine is 42. At the end of the original "The Hitchhiker's Guide To The Galaxy" radio show Arthur uses a travel Scrabble set to spell out "The Ultimate Question to The Meaning Of Life The Universe And Everything"(the answer of which is 42) and comes up with "What is Six times Nine?".
Can absolute error be negative?
No because taking the absolute value of a number always yields a positive value.
Examples of relative frequency?
- Count A = the number of dumb questions that I see on this site.
- Count B = the total number of questions that I see on this site.
- Then the relative frequency of dumb questions that I see on this site is A/B.
What is the answer to 8349 in base 4?
834910 = 20021314
To find that, start dividing 8349 by 4, over and over again, rounding down, and write the remainders down in reverse order, until you get to a quotient of zero.
Another way, which is actually what I did, is to use the Windows Calculator in scientific mode and convert 834910 into 100000100111012. Since 4 is a power of 2, you can use the trick of grouping the bits. This gives you 10 00 00 10 01 11 01, and by inspection you can see that the answer is 2002131.
All branches of mathematics are of use today. Everything around you has a large dependency on Maths. Your computer is built on a whole range of mathematical principles in more ways than you can imagine. Algebra features amongst many aspects of mathematics, far too many to outline.
What is the symbol used for quotient?
To my knowledge, there is no symbol used for quotients in mathematics.
How many digits are used in a binary number system and what are they?
There are two digits in the binary number system. 0 and 1
How may distinguishable permutations are possible with all the letters of the word ellises?
We can clearly observe that the word "ellises" has 7 letters and three pairs of letters are getting repeated that are 'e','l' and 's'. So, Number of distinguishable permutations = 7!/(2!2!2!) = 7 x 6 x 5 x 3 = 630.
What is the value of 5 minus 5 over 3 plus 5 over 9 minus 5 over 27?
5 - 5/3 + 5/9 - 5/27 + ... = 5 + 5(-1/3)¹ + 5(-1/3)² + 5(-1/3)³ + ...
The required sum is an infinite GP with initial term a = 5, and common difference r = -1/3
As |r| < 1, the sum can be found from sum = a/(1 - r)
→ 5 - 5/3 + 5/9 - 5/27 + ...
= 5/(1 - (-1/3))
= 5/(1 + 1/3)
= 5/(4/3)
= 5 × 3/4
= 15/4
= 3¾
What does A built-in calculation such as SUM or AVERAGE called?
That's called a built-in function; or often simply a "function".
What are the limitations of using newton-raphson method?
There are several limitations to the Newton-Raphson method (N-R).
1. The method relies on the use of the derivative of the function whose root is being sought. If the function is not differentiable then N-R cannot be used. Even if the derivative exists, it may not be calculable analytically. In that case N-R may require huge amounts of effort or prove to be impossible.
2. If there is a stationary point in the vicinity of the root, the derivative will become 0 at that point and attempted division by zero will stop N-R. Even if the iteration does not actually hit the stationary point, the rounding errors due to division by a very small number can lead to very large errors in the N-R calculations.
3. If the first derivative is ill-behaved in the neighbourhood of the root then N-R can overshoot. For example, f(x) = |x|^a where 0 < a < 1/2.
4. A poor starting point for the N-R iteration can lead to non-convergence.
5. Where a root has a multiplicity greater than 1, then convergence will be slow (unless appropriate adjustments are made to N-R).
A sparse matrix is a matrix in which most of the elements are zero.
Why we draw tangent in newton raphson method?
A line tangent to a curve, at a point, is the closest linear approximation to how the curve is "behaving" near that point. The tangent line is used to estimate values of the curve, near that point.
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m1w3m2w2m3w1
m1w1m3w2m2w3
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m1w2m3w3m2w1
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m2w1m3w2m1w3
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from itertools import permutations m = permutations(range(1,4)) w = permutations(range(1,4)) poss = [ ] for p_m in m : w = permutations(range(1,4)) for p_w in w : item = 'm%sw%sm%sw%sm%sw%s' % \ ( p_m [ 0 ], p_w [ 0 ], p_m [ 1 ], p_w [ 1 ], p_m [ 2 ], p_w [ 2 ], ) if not item in poss : poss . append ( item ) for item in poss : print item
Is a to the 3rd power greater than or equal to a for all integer values of A and why?
No. A negative integer raised to the third power will yield a negative number that is less than the integer. Only whole numbers (positive integers greater than or equal to 1) have the property where that integer raised to the third power is greater than or equal to the integer.
What is the median if there is only 2 numbers showing?
Technically, you cannot find a median if you have only two numbers, so it would be more reasonable to use an average instead.
How does 2 plus 2 equals Fish 3 plus 3 equals Eight 7 plus 7 equals Triangle?
When you take the two numbers and put them together as an image you can come up with your results.
How do you caluculate the GCD of two prime numbers?
Let p1 and p2 be the two prime numbers.
Because they are prime, their divisors are div(p1) = {1,p1} and div(p2) = {1,p2}. So GCD(p1,p2) = Greatest Common Divisor of p1 and p2 =
p1 if p1 equals p2
1 if p1 is different from p2
How do you minimise errors in numerical integration?
Increase the number of segments into which the domain is divided. In particular, increase them where the function has the greatest absolute gradient.
What is advantages of bisection method?
In the absence of other information, it is the most efficient.
