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Questions tagged [computational-mathematics]

This tag concerns computational problems central to mathematical and scientific computing. The scope includes algorithms, numerical analysis, optimization, and linear algebra, computational topology, computational geometry, symbolic methods, and inverse problems.

Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Subtopics include numerical linear algebra, numerical optimization, computational geometry, numerical PDEs and inverse problems.

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1945 questions
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Computational Maths - Normalised mantissa

What does overflow and underflow of an normalised mantissa mean?
user140152
  • 187
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Jacobi Iteration Question

I have a question that says use a relative tolerance of $10^{-3}$ and asks if the estimate errors are in line with the actual errors. What does relative tolerance mean and how do you work out estimate errors? Assuming actual error is the…
user140152
  • 187
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Calculate roll length based on inner/outer diameter and number of turns.

I have seen in this link that there is a way to calculate the rolled material length and the number of turns based on: the material thickness inner diameter of the roll external diameter of the roll Is there a way to calculate the length of a…
Marinos An
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summation in pari gp

Is there any command to evaluate in PARI GP such sum: $\sum\limits_{\substack{2\leq d\leq n \\ (d, n)=1}}\frac{a\left(n \right)}{d}$ ? In other words: how to add to command sum(d=2, n, \frac{a(n)}{d}) condition from second line ($(d,n)=1$).(or more…
Adrian
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Why is Horner's method for evaluating polynomials not suitable for root finding?

$$ p = \sum_{k = 0}^n a_k x^k $$ Horner's method for evaluating a polynomial: $$ \begin{align} p_H &= a_0 + x \left( a_1 + x \left( a_2 + x \left( a_3 + .... + x \left( a_{n -1} + x a_n \right) \right) \right) \right) \\ &... \\ & = a_0 + x…
Belen
  • 568
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Newton method - speed of convergence

Let $x_0 \neq 0$ lies in the convergence ball of the solution $\alpha=2$ for the equation: $f(x)=0$ where $f(x):=x^3-5x^2+8x-4$ What will be the convergence speed of Newton's method? I did it this way: Let…
frugo
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Did I do the task correctly?

A fisherman on a boat sailed against the current of the river, an empty flask fell from the boat into the river near the bridge. After that, having sailed $15$ minutes against the current of the river, the fisherman noticed his loss and swam in the…
марат
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Find rate when changing discount and vice-versa while keeping a fix final price

I am a web developer and building an accounting system for a client however I am almost good at programming but very bad at accounting and maths; and my client is not able to explain/communicate properly and present the equation of the calculations.…
Nikunj Bhatt
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How could I prove that L1 is undecidable?

The Problem: Let L1 = {Kod(M) | M is a TM and when started with a blank input tape, M eventually writes a 1 somewhere on the tape } Prove that L1 is undecidable. I have the following 2 TMs whcih I have proved are undecidable to help me prove the…
jreyes
  • 111
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Why is the gradient summed in a computational graph for an operation with split output?

I was looking at back propagating a gradient through a computational graph, and all makes sense aside from when a node has multiple outputs. Take the following function: $$f(x) = (x+3)(x+2)$$ Which obviously has the derivative: $$f'(x) = 2x+5$$ Now,…
Recessive
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How do I become better at reading lemmas and algorithims?

This may be a bit of a strange question but whenever I am confronted by a block of algorithms I get quite annoyed and confused (example below). It seems to me that the way of explaining concepts using mathematical symbols that I usually find not…
Ace
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How to find a close form expression in terms generating functions for the triple summation

Given $$\sum\limits_{i=0}^\infty a_i z^i=A(z)$$ and $$\sum\limits_{i=1}^\infty b_i z^i=B(z)$$ and $$\sum\limits_{i=0}^\infty c_i z^i=C(z)$$ Find $\sum\limits_{i=1}^\infty\sum\limits_{j=0}^\infty a_j \sum\limits_{k=1}^\infty b_kc_{k+j-i} z^i$ in…
Litun
  • 670
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Fast way to manually compute exponents (interest, probability)?

When doing financial, actuarial or probability calculations, often a person is faced with computing exponentiations. For example, let's say the chance of a particular ship sinking is 1% per year. Then to compute the chance of the ship sinking over…
Tyler Durden
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Efficiently computable, nonempty sets with no known element

I'm looking for sets $S$ of natural numbers with the following properties: There is a known efficient algorithm for determining whether a given $n$ is in $S$ (let's say "efficient" means polynomial in the number of digits of $n,$ with reasonable…
Elliot Glazer
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Making an expression stable for small values

The following expression shows significant numerical differences in a program when I compile in x86 (32 bit) versus x64 (64 bit), when $a$ is small: $$ \left( \dfrac{1}{a} - b \right) \left( 1- \exp(-a)\right)$$ Is there a way that I can refactor…
RoG
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