# Questions tagged [mathematical-analysis]

Questions related to mathematical analysis (often called analysis by mathematicians)

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### How to solve recurrence. T(n). = T(n-1) + T(n/2) + n?

I am aware that to get a running time by recursion tree method, we need to draw a tree and find: a) number of levels in tree. Since left side of tree decreases by 1 in size, so it's longest path ...
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### Decryption of RSA

How can we decrypt an RSA message if we only have the public key? For example, Message: 21556870,12228498 Public Key: ...
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### I don't understand formula meaning of computer vision Paper

I am master degree student at Computer Science Department. I started master degree at this year. Now I'm reading two papers about computer vision. Actually before time I didn't have experience about ...
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### Why postfix is used more often than prefix expression?

i was reading stack and i came across the infix, preifx and postfix expression.So i understood that why postfix /prefix expressions are preferred over infix expression ( due to its unambiguous nature) ...
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### Finding the count of 0's bounded by all 1's

Given N * M 2-D matrix find out all the 0's which are completely bounded by the all 1's. ( This is not any online platform question ) (This problem statement I faced during an interview). Sub-matrix ...
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### Number of permutations of set {1, 2, …, n} for which insertion sort will perform exactly n permutations

I have had the following problem at my last exam: For how many permutations of set {1, 2, ..., n} where n > 2 will insertion sort (without guard element) perform exactly n comparisons. My thinking ...
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### If we can $\epsilon-$cover one set with $\frac{K}{2}$ elements and another with 2 elements why isn't their set product $2^{\frac{K}{2}}$ cover?

I was reading the following paper on Robustness and Generalization (and covering numbers)and I was reading their example 1: which didn't quite make sense to me. The reason it didn't make sense is ...
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### Can someone explain why there are two summations here?

The following quote is from the book "The art of computer programming": (..) sentence would presumably be used only if either $j$ or $k$ (not both) has exterior significance. In most cases we ...
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### Minimizing $E_{out}$ theoretically in linear regression

Related to linear regression with noise I've been given the following functional, depending on the function $h$: $$E_{out}(h) = \int \int (h(x)-y)^2 dx dy$$ I want to prove that the function that ...
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### Estimating the run time of a program according to a given CPU performance

When we have a recurrence relation of a program, as an example: T(N) = N log N + 9N + 55 and the CPU capability let's say (10^6) or any other number. What is ...
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### Why is the number of comparisons in a BST missing key lookup about 2 ln N?

In (An Introduction to the Analysis of Algorithms) by Philippe Flajolet and Robert Sedgewick it's written that: Insertions and search misses in a BST built from N random keys require ~ 2 ln N (about 1....
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### Relationship between lexicographic index of size k (tuple) with that of size(k-1) tuple

Given a non-negative integer $n$ such that $X = \{1,2, \dots, n\}$, a combination of k-tuple and its associated index $pos_k$. How to compute the associated lexicographic index for any subset of the ...
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### Analysis of the long division algorithm in the Knuth book (Seminumerical algorithms) 1

I've been reading through the long division algorithm exposed in the Knuth book for a week and I still miss some details. There's an implementation of such algorithm in "Hacker's Delight" by Warren, ...
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### Set of all rational numbers less than given computable real number is decidable

Prove that set of rational numbers less than given computable real number is decidable This problem was in my exam yesterday, but I was not able to solve it. However I still want to give it another ...
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### Do formulas involving fewer repetitions of variables give higher numerical precision?

I'm having some trouble doing SICP exercise 2.15. Please note that this question is not closed related to Lisp. Instead, it's closely related to numerical analysis. Exercise 2.15. Eva Lu Ator, ...
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### Hash function to hash 6-digit positive integers

Let UID denote a unique identifier. UID's are represented as 6-digit positive integers. I want to insert a collection of UID's in a hash table with $M$ buckets, where $M$ is a prime number (for ...
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### Yarn Resource Allocation

Say for an example,i have Color codes that are : A , B , C I want to repeat this colors so i ll put them as : 5A , 10B , 10C = 25 So now A will repeat 5 times ,B will repeat 10 times and C will repeat ...
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### Why does russian peasant multiplication work? [duplicate]

can someone provide a proof with induction on why the Russian peasant multiplication work ? if you don't know what that is , here is the algorithm : ...
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### Derivative for x-direction for image

I want to ask, consider we want to compute the slope of x-direction of the following step . The slope for it would be $m =\frac{0}{m_2 - m_1} =\frac{0}{5 - 2}$ which is 0. But the derivate for ...
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### How to prove with induction [duplicate]

So far I have learned how to write proofs by induction and it went fine until I got this recursive problem, which I'm not quite sure how to begin and how to prove that with induction. ...
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### Abs(sum of differences of elements in a sorted array) = array.Max()-array.Min() Why?

I just found out by luck that Abs(sum of differences of elements in a sorted array) = array.Max()-array.Min() For example, Consider a sorted array, {1 43 65 97 ...
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### Reference request: Introduction to reinforcement learning with hand calculation examples

For me, the most difficulty when it comes to learning about reinforcement learning is that there is not much to learn in the sense that without running some algorithm, it is very difficult to get a ...
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### How to calculate an accurate estimated reading time of text?

I suppose the calculation should not be done by only two factors (average reading speed/words per minute, and word count). But at least by a third parameter, that in my opinion should measure the ...
Let's suppose I have two functions $F$ and $G$ and I'm interested in determining whether $$F(x) = \int G(x)dx.$$ Let's suppose that my functions are composed of elementary functions (polynomials, ...