Questions tagged [na.numerical-analysis]

13 questions with no upvoted or accepted answers
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10
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97 views

Complexity of checking $a > br^m + cr^n$, with $r$ rational

I'm wondering if the following problem is decidable in P-time (or even NP): Given $a, b, c \in \mathbb{Z}$ and $m, n, p, q \in \mathbb{N}$ all in binary, decide if $a > br^m + cr^n$, where $r = {p ...
8
votes
0answers
361 views

Efficiently approximating derivative of a well-behaved function

I need an algorithm for adaptive sampling a well-behaved function and computing its derivative in the sampling range with prescribed accuracy. The function has no more than one minimum in the sampling ...
7
votes
0answers
128 views

What's the state of the art for matrix nuclear/trace norm optimization

I am interested in simple matrix optimizations with nuclear/trace norm: $\min_X \left(f(X) + \|X\|_*\right)$ where $\|X\|_*$ stands for the trace norm of the matrix $X$, and $f$ is a convex smooth ...
7
votes
0answers
134 views

What's new in sparse eigensystems solution

As a part of other work I need to solve relatively large (~1E5x1E5) and sparse (~100 non-zero elements in each raw in few blocks) hermitian eigensystems. Usually only few eigenvalues+vectors are ...
3
votes
0answers
61 views

Monotonic and bounded sequences throughout computer science

When I refer to the Monotone Convergence Theorem below, I refer to the very simple claim that if a non-decreasing sequence has an upper bound then it converges. I don't refer to the claim from Measure ...
3
votes
0answers
80 views

Efficiently Detecting “edges” in the time frequency plane

Given a signal $y(t)\in\mathbb{R}$ I wish to detect edge patterns. $s(f,t)$ is a time-frequency decomposition of $y(t)$ in some window $(t-n,t+n)$ so that $f$ loosely corresponds to a local frequency....
2
votes
0answers
341 views

Is there any algorithm to find just the largest eigenvalue with subquadratic time complexity?

SVD or PCA can be used find the largest eigenvalue, but at a cost of $O(n^3)$ complexity. Lanczos algorithm runs much faster on a sparse matrix with complexity $O(dn^2)$ where $d$ is the average ...
2
votes
0answers
391 views

the confusion about 'with high probability (w.h.p.)'

w.h.p. can often be seen in the analysis of randomized algorithms. It's definition can be seen here https://en.wikipedia.org/wiki/With_high_probability. However my confusion is that: Assuming we ...
1
vote
0answers
163 views

How can I understand the Coppersmith–Winograd algorithm?

I want to do research on matrix multiplication algorithms. I glanced at the Coppersmith-Winograd algorithm paper, but I didn't understand anything. How can I complete the background to read this paper?...
1
vote
0answers
90 views

Complexity of low-rank matrix factorizations with rows in a simplex and outliers

Our goal is to obtain a matrix factorization in form of $M = U V'$, where $U\in\mathbb{R}^{d\times r}, V \in\mathbb{R}^{N\times r}$ and each row of $V$ satisfies $$ \sum_{j}(V)_{ij}=1, (V)_{ij}\ge 0 $$...
1
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0answers
103 views

Computing log of sum of positive integers

As input, we are give $k$-bit approximation (after the decimal point) of $\log(a)$ and $\log(b)$ for positive integers $a$ and $b$, i.e, we are given $\alpha$ and $\beta$ (as binary strings) as input ...
1
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0answers
58 views

Computational complexity of Initial Value Problems of ODEs

Are there known results on computational complexity of initial value problems of ODEs? As my question may be somewhat vague, I want to mention that I'm mainly interested for results on the ...
1
vote
0answers
120 views

High Dimensional Volume (HDV) estimator for Entropy estimation

I am writing a program using high-dimensional volume (HDV) estimator to estimate entropy and mutual information for variable selection. Let $ D = (x^i_1, x^i_2, ..., x^i_M)$, N is the number of data ...