Questions tagged [mathematical-analysis]
Questions related to mathematical analysis (often called analysis by mathematicians)
126 questions
0 votes
0 answers
50 views
How to theoretically analyze the convergence of the Raccoon Optimization Algorithm?
I’m studying the Raccoon Optimization Algorithm (ROA), a metaheuristic inspired by the foraging behavior of raccoons. (Proposed by Joohi et al. 2018). While empirical results show promising ...
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3 votes
1 answer
405 views
Finding the solution to an equation closest to an arbitrary state
There are a number of numerical methods for finding a solution to an equation that is usually close to the initial guess, but not always the closest. Is there an algorithm that will always find the ...
1 vote
0 answers
45 views
Mathematically deriving the ultimate activation function
I have been working on finding the ultimate activation function here are the properties I would suspect the function to have: Positive lipshitz continuous, i.e $0 \leq f'(x) \leq 1 \; \forall x\in \...
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1 vote
0 answers
39 views
Error in formula for choosing noise multiplier $\sigma$ in DP-SGD based on Gaussian Mechanism?
While reviewing the literature on differential privacy and its addition to ML, I noticed that I do not end up with the same formula for the noise multiplier $\sigma$ for the differentially-private SGD ...
3 votes
0 answers
49 views
Is this approach to generating points for the graph of a function that attempts to avoid discontinuities appropriate?
I'm not sure where to ask this question, I'd appreciate being redirected accordingly if need be. Context Let's say I have a program that might plot the graph of functions supplied by a user, for ...
- 300
1 vote
1 answer
74 views
Proving $f(n) = 1 + c + c^2 + \cdots + c^n = \Theta(1) $
How can I prove that the function $$ f(n) = 1 + c + c^2 + \cdots + c^n $$ is $\Theta(1)$ when $c<1$? where $n \in \mathbb{N}$ and $c \in \mathbb{R}$, with $c>0$. Can I use limits? Thank you in ...
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0 votes
1 answer
271 views
Struggling with Recurrence Relation using Telescoping Approach
I have the following recurrence relation that I am trying to solve using the telescoping approach: $T(n) = \begin{cases} T(\frac{n}{4})+ n^2 & \text{for } n \geq 4 \\ 1 & \text{otherwise} \...
1 vote
1 answer
147 views
Understanding crossover points in efficiency between insertion and merge sorts
Self-taught programmer here. I'm reading CORS, and right at the beginning, question 1.2-2, there asks a question: For inputs of size $n$, insertion sort runs in $8n^2$ steps, which merge sort runs in ...
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0 votes
1 answer
136 views
Consider A Busy Beaver like Turing Machine on a Mobius Strip. Is it equivalent to standard BB number?
I have modified Busy Beaver Turing Machine scenario. Is this new scenario equivalent to the standard one? Consider a double sided tape twisted it into a mobius strip having P slots in total. Initially ...
- 111
-1 votes
1 answer
856 views
Design an algorithm to predict words based on a skeleton from a given dictionary
I'm working on an algorithm which is permitted to use a training set of approximately 250,000 dictionary words. I have built and providing here with a basic, working algorithm. This algorithm will ...
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1 vote
1 answer
882 views
Finding equal-sum subsets from two arrays
Consider the following problem: You are given two integer arrays $A$ and $B$ of size $N$ and $M$, respectively. You are guaranteed that $1 <= A[i] <= M$ and $1 <= B[i] <= N$ for all $i$ (...
2 votes
1 answer
134 views
Finding an approximate double-zero using binary search
Let $f$ be a continuous real function on $[-1,1]$. The function is accessible via queries: for any $x$, the value of $f(x)$ can be computed in constant time. If $f(-1)<0$ and $f(1)>0$, then by ...
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0 votes
1 answer
238 views
Is "Bitwise Complement Operator" (~ tilde) distributive?
To be more precise, Is ~(a+b) = ~a + ~b? Here, "~" bitwise NOT operator. I ran into this question while thinking about ...
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-6 votes
1 answer
83 views
How to solve this recurrence relation: T(n) = R(n-1) + n log n R(n) = T(n-1) + n^2
How to solve this recurrence relation: T(n) = R(n-1) + n log n R(n) = T(n-1) + n^2
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0 votes
0 answers
115 views
Proving an asymptotic bound with induction
Suppose we want to prove by induction that $f(n) \in \Theta(g(n))$. How should the induction proof be set up? I'm tempted to say that the base case should prove that $f(1) \in \Theta(g(1))$ and the ...
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