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2
votes
0answers
31 views

0 error interpolation for discrete finite value points

I am working on an algorithm that requires me to interpolate a couple trillion positive discrete points with f(x) having low finite value (for example 0 - 5). It there a specialized algorithm specific ...
0
votes
1answer
37 views

Can someone interpret what this is asking for

I have this programming problem, but I really cant figure out what it wants me to do. Heres what it is: The cube root of a number can be found based on the observation that, if $t$ is an ...
3
votes
1answer
94 views

Is “ternary search” an appropriate term for the algorithm that optimizes a unimodal function on a real interval?

Suppose that I want to optimize a unimodal function defined on some real interval. I can use the well-known algorithm as described in Wikipedia under the name of ternary search. In case of the ...
0
votes
0answers
39 views

Numerically approximating an inverse integral transform?

My question is about numerical methods for inverting integral transforms; I'm trying to numerically invert the following integral transform: $$F(y) = \int_{0}^{\infty} y\exp{\left[-\frac{1}{2}(y^2 + ...
1
vote
0answers
59 views

Error accumulation in a numerical integration

I have this problem: Consider the problem of calculating the integral $$y_n =\int_{0}^{1} \dfrac{x^n}{x+10} \mathrm{d}x $$ for a positive integer $n$. Observe that $$y_n + 10y_{n-1} = ...
1
vote
0answers
62 views

Does Automatic Differentiation handle conditional branches, if yes how?

I'm trying to understand how Automatic Differentiation (AD) works. For simple algebraic operation, I get the chain rule thing. But, when the code contains conditional statement like ...
2
votes
1answer
63 views

What are the drawbacks of using an algorithm that is not backwards stable?

(This question might be legitimately crossposted to stackoverflow or mathoverflow or programming StackExchanges.) Preface I'm reading this paper on solving linear systems of equations ...
6
votes
2answers
79 views

numerical integral vs counting roots

I have a problem that can be viewed in two different ways: Compute an $n$-dimensional integral, numerical context. The domain of integration is an $n$-dimensional hyper-cube of side $L$. Count (just ...
13
votes
2answers
248 views

Computing inverse matrix when an element changes

Given an $n \times n$ matrix $\mathbf{A}$. Let the inverse matrix of $\mathbf{A}$ be $\mathbf{A}^{-1}$ (that is, $\mathbf{A}\mathbf{A}^{-1} = \mathbf{I}$). Assume that one element in $\mathbf{A}$ is ...
0
votes
2answers
109 views

Implications of truncation of numbers when converted into binary

I have been posed with a question whereby a computer truncates numbers to x number of digits. Due to this, if this computer is trying to store a decimal number which has a binary equivalent greater ...
3
votes
4answers
338 views

Algorithms computing if a number is a multiple of 3

When doing mental calculus one can do: Given an integer k, sum all the digits (in base 10), and if the result is a multiple of 3, then k is a multiple of 3. Do you know of any algorithm working ...
0
votes
1answer
271 views

In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes

In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes Floating point overflow. Negative floating point overflow. All 0's in the exponent ...
7
votes
0answers
199 views

Alternatives to SVD for rank factorization

I have rank-deficient matrix $M \in \mathbb{R}^{n\times m}$ with $\text{rank}(M) = k$ and I want to find a rank factorization $M = PQ$ with $P \in \mathbb{R}^{n \times k}$ and $Q \in \mathbb{R}^{k ...
4
votes
0answers
279 views

Arc-Length parameterization of a cubic bezier curve

I like to implement an arc-length Parameterization of a cubic bezier curve. So far I have implemented the method of calculating the arc length of the curve and now I'm stuck at calculating the times ...
11
votes
1answer
193 views

Floating point rounding

Can an IEEE-754 floating point number < 1 (i.e. generated with a random number generator which generates a number >= 0.0 and < 1.0) ever be multiplied by some integer (in floating point form) to ...
1
vote
0answers
81 views

Which method for ODE instead of Euler's?

I need a super-fast method for ordinary differential equations. Should I use the midpoint method? I need this for a reaction-diffusion system (Gray-Scott).
3
votes
1answer
100 views

An argument for error accumulation during complex DFT

I am doing FFT-based multiplication of polynomials with integer coefficients (long integers, in fact). The coefficients have a maximum value of $BASE-1, \quad BASE \in \mathbb{n},\quad BASE > 1$. ...
4
votes
1answer
216 views

Fast Poisson quantile computation

I am seeking a fast algorithm to compute the following function, a quantile of the Poisson distribution: $$f(n, \lambda) = e^{-\lambda} \sum_{k=0}^{n} \frac{\lambda^k}{k!} $$ I can think of an ...
3
votes
0answers
257 views

Cyclic coordinate method: how does it differ from Hook & Jeeves and Rosenbrock?

I have trouble understanding the cyclic coordinate method. How does it differ with the Hook and Jeeves method and the Rosenbrock method? From a past exam text: Describe the cyclic coordinate ...
7
votes
2answers
202 views

Detecting overflow in summation

Suppose I am given an array of $n$ fixed width integers (i.e. they fit in a register of width $w$), $a_1, a_2, \dots a_n$. I want to compute the sum $S = a_1 + \ldots + a_n$ on a machine with 2's ...
10
votes
1answer
171 views

Overflow safe summation

Suppose I am given $n$ fixed width integers (i.e. they fit in a register of width $w$), $a_1, a_2, \dots a_n$ such that their sum $a_1 + a_2 + \dots + a_n = S$ also fits in a register of width $w$. ...