Matrix algorithms. Medical search. Frequent questions

Our algorithm computes the sparse matrix approximation in a single pass over the data. (satyenkale.com)
This paper addresses matrix approximation problems for matrices that are large, sparse, and/or representations of large graphs. (ibm.com)
Drineas, P., Kannan, R. & Mahoney, M. W. Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix. (nature.com)

Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms efficient. (wikipedia.org)
Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems such as counting the paths through a graph. (wikipedia.org)
Directly applying the mathematical definition of matrix multiplication gives an algorithm that takes time on the order of n3 field operations to multiply two n × n matrices over that field (Θ(n3) in big O notation). (wikipedia.org)
Better asymptotic bounds on the time required to multiply matrices have been known since the Strassen's algorithm in the 1960s, but the optimal time (that is, the computational complexity of matrix multiplication) remains unknown. (wikipedia.org)
As of October 2022[update], the best announced bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.37188) time, given by Duan, Wu and Zhou announced in a preprint. (wikipedia.org)
The three loops in iterative matrix multiplication can be arbitrarily swapped with each other without an effect on correctness or asymptotic running time. (wikipedia.org)
An alternative to the iterative algorithm is the divide-and-conquer algorithm for matrix multiplication. (wikipedia.org)
The divide-and-conquer algorithm computes the smaller multiplications recursively, using the scalar multiplication c11 = a11b11 as its base case. (wikipedia.org)
To solve $A' x = b$, in addition to matrix multiplication, we need to make two calls to the tridiagonal system. (sarawak.com.my)

Making use of traditional dietary recommendation algorithm researches, we combine the Adaboost classifier with probabilistic matrix factorization. (techscience.com)
We present a personalized diet recommendation algorithm by taking advantage of probabilistic matrix factorization via Adaboost. (techscience.com)
A probabilistic matrix factorization method extracts the implicit factors between individual food preferences and nutritional characteristics. (techscience.com)
In computer science and operations research , the ant colony optimization algorithm ( ACO ) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs . (wikipedia.org)
The methods, including an adaptation of the cross correlation algorithm, the generic edit distance algorithm, the edit distance algorithm with a probabilistic substitution matrix, Bayesian analysis, and Bayesian analysis on an actively thinned reference dictionary were implemented and their accuracy rates compared. (nih.gov)

A common simplification for the purpose of algorithms analysis is to assume that the inputs are all square matrices of size n × n, in which case the running time is Θ(n3), i.e., cubic in the size of the dimension. (wikipedia.org)
The square matrices has two diagonals primary(right to left) and secondary(left to right) diagonals of equal length. (tutorialspoint.com)

Application of the master theorem for divide-and-conquer recurrences shows this recursion to have the solution Θ(n3), the same as the iterative algorithm. (wikipedia.org)
Is this true or does the reordering affect the convergence/accuracy of the iterative algorithm? (stackexchange.com)

EN] Trigonometric matrix functions play a fundamental role in second order differential equations. (upv.es)
Tridiagonal Matrix Algorithm A. Salih Department of Aerospace Engineering Indian Institute of Space Science and Technology, Thiruvananthapuram { October 2010 {A system of simultaneous algebraic equations with nonzero coe cients only on the main diagonal, the lower diagonal, and the upper diagonal is called a tridiagonal system of equations. (sarawak.com.my)
A tridiagonal system for n unknowns may be written as In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. (sarawak.com.my)
Tridiagonal matrix algorithm From Wikipedia, the free encyclopedia The tridiagonal matrix algorithm (TDMA), also known as the Thomas algorithm, is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. (sarawak.com.my)
It is a very active research topic to study solutions to various matrix equations [ 1 - 4 ]. (hindawi.com)
1393). A numerical algorithm for solving a class of matrix equations. (ac.ir)
1393). 'A numerical algorithm for solving a class of matrix equations', فیزیولوژی و بیوتکنولوژی آبزیان , 2(1), pp. 41-54. (ac.ir)
In this paper, we propose an improved preconditioned algorithm for the conjugate gradient squared method (improved PCGS) for the solution of linear equations. (scirp.org)
These bi-Lanczos-type algorithms are very important because they are often adopted to solve the systems of linear equations that arise from large-scale numerical simulations. (scirp.org)

The non-binary biclustering algorithms can process gene expression data directly, such as Local Search Algorithms (LSM) [ 16 ], while binary biclustering algorithms convert gene expression data into a binary data matrix before processing the expression dataset. (biomedcentral.com)
[2] Combinations of artificial ants and local search algorithms have become a method of choice for numerous optimization tasks involving some sort of graph , e.g., vehicle routing and internet routing . (wikipedia.org)

T ( n ) = 8 T ( n / 2 ) + Θ ( n 2 ) , {\displaystyle T(n)=8T(n/2)+\Theta (n^{2}),} accounting for the eight recursive calls on matrices of size n/2 and Θ(n2) to sum the four pairs of resulting matrices element-wise. (wikipedia.org)
In this paper, we propose a recursive algorithm, RecurJac, to compute both upper and lower bounds for each element in the Jacobian matrix of a neural network with respect to network's input, and the network can contain a wide range of activation functions. (aaai.org)

9 ], is a divide-and-conquer algorithm that yields a maximal binary submatrix in which important information represents 1 or 0. (biomedcentral.com)

I've written up the mathematical algorithm in this article. (sarawak.com.my)
This improved PCGS algorithm retains some mathematical properties that are associated with the CGS derivation from the bi-conjugate gradient method under a non-preconditioned system. (scirp.org)

After feeding a connectivity matrix into METIS and reordering the nodes (I have zero knowledge of the theory behind what it does), my sparse matrix-vector products (intel MKL) were about 30% faster, with the same numerical results and number of iterations for my conjugate gradient solver. (stackexchange.com)
When you take the LU factorization of a sparse matrix, the L and U factors might lose some of its sparsity, the extra entries are called fill in. (stackexchange.com)
We describe a simple random-sampling based procedure for producing sparse matrix approximations. (satyenkale.com)
Davis, T.A. The University of Florida Sparse Matrix Collection. (scirp.org)

In this article, we will learn how to write a swift program to compute the sum of diagonals of a matrix. (tutorialspoint.com)
So either using nested or single for loop we can compute the sum of the diagonals of a matrix. (tutorialspoint.com)
Optimal Algorithms to Compute the Closure of a Set of Iso-Rectangles. (uni-trier.de)

For well conditioned matrices this is better than inverting $A$ in $O(n^\omega)$ time (as well as various matrix factorization algorithms. (stackexchange.com)

A Linear Algorithm for Nonhomogeneous Spectra of Numbers. (uni-trier.de)

Parallel algorithms: General principles. (routledge.com)

In this project Dr Blumensath will develop new computer algorithms to analyse data that arises, for example, in brain imaging. (southampton.ac.uk)

Our numerical experiments show that the performance of the methods depends strongly on the problem, but that, among our tested methods, the spectral projected gradient method is the clear winner.In the second part we look at two two-sided optimization problems where the matrix of unknowns $Y\in\R^{n\times p}$ lies in the Stiefel manifold. (manchester.ac.uk)
We propose an augmented Lagrangian-based algorithm that uses these geometric tools and allows us to optimize an arbitrary smooth function over $\mathcal{C}$. This algorithm can be used to select a particular solution out of the latter set $\mathcal{C}$ by posing a new optimization problem. (manchester.ac.uk)
As an example, ant colony optimization [3] is a class of optimization algorithms modeled on the actions of an ant colony . (wikipedia.org)
Nonetheless, we show that certain linear images of $\text{SO}(n)$ are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. (optimization-online.org)

Many different algorithms have been designed for multiplying matrices on different types of hardware, including parallel and distributed systems, where the computational work is spread over multiple processors (perhaps over a network). (wikipedia.org)
If I understand correctly, the reordering algorithm optimizations are purely computational: the goal is to come up with a storage of the matrix more adequate for caching effects. (stackexchange.com)
The proposed algorithm has a high computational efficiency. (ac.ir)
Our objective is to employ matrix completion to reduce computational effort associated with the calculation of multiple quantum chemical Hessians, which are necessary for identification of temperature-dependent free energy maxima under canonical variational transition state theory (VTST). (aip.org)
Understanding whether quantum machine learning algorithms present a genuine computational advantage over classical approaches is challenging. (nature.com)
Researchers have put forth many proposals to gain a computational advantage with quantum machine learning (QML) algorithms for domains ranging from recommendation systems 1 to topological data analysis 2 , but these proposals typically require unique assumptions that make the comparison to classical algorithms difficult. (nature.com)

My implementation includes a volatility-targeting binary search algorithm. (r-bloggers.com)

An O(N²) Algorithm for Coloring Perfect Planar Graphs. (uni-trier.de)

M/b cache lines), the above algorithm is sub-optimal for A and B stored in row-major order. (wikipedia.org)
Initially proposed by Marco Dorigo in 1992 in his PhD thesis, [6] [7] the first algorithm was aiming to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food. (wikipedia.org)
An Optimal Contour Algorithm for Iso-Oriented Rectangles. (uni-trier.de)
However, IMPALA employs a more refined analysis of statistical significance and, unlike PSI-BLAST, guarantees the output of the optimal local alignment by using the rigorous Smith-Waterman algorithm. (nih.gov)

Sampling and multilevel coarsening algorithms for fast matrix approximations for Numer. (ibm.com)
A multilevel coarsening technique is proposed, which utilizes a hypergraph associated with the data matrix and a graph coarsening strategy based on column matching. (ibm.com)

From a broader perspective, ACO performs a model-based search [8] and shares some similarities with estimation of distribution algorithms . (wikipedia.org)
In this paper, an improved algorithm is proposed for mixing matrix estimation in underdetermined blind source separation (UBSS). (yhxb.org.cn)
Then, those single source points which deteriorate the mixing matrix estimation accuracy are removed. (yhxb.org.cn)
A Robust Underdetermined Mixing Matrix Estimation Algorithm[J]. Journal of Astronautics, 2013, 34(3): 426-433. (yhxb.org.cn)
Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required? (stackexchange.com)

If I understand correctly, I need to encode eigenvalues of a $2 \times 2$ matrix $A$ , say $\lambda_1$ and $\lambda_2$ in the quantum register. (stackexchange.com)
Is finding Eigenvalues of matrix $A$ supposed to be a classical subroutine? (stackexchange.com)
Finding the eigenvalues of $A$ is an intermediate part of the HHL algorithm (although it will not output them). (stackexchange.com)
We demonstrate proof-of-principle of an algebraic variety-based matrix completion method for recovering missing elements in a matrix of transverse Hessian eigenvalues constituting the minimum energy path (MEP) of a reaction. (aip.org)
We demonstrate that, with as low as 30% random sampling of matrix elements for the largest system in our test set (46 atoms), the complete matrix of eigenvalues can be recovered. (aip.org)

We examine several algorithms for solving the nearness problem that differ in whether or not they can take account of the nonlinear constraints and in their convergence properties. (manchester.ac.uk)

begingroup$ Do you realize the Cuthill-Mckee algorithm was published back in 1969? (stackexchange.com)
begingroup$ @CharlieS Are you referring to METIS' fill reducing matrix ordering or mesh partitioning function? (stackexchange.com)

Detection and Tracking Algorithm for Small Infrared Target on Missile Borne Platform [J]. Journal of Astronautics, 2020, 41(11): 1440-1448. (yhxb.org.cn)

Given a matrix over the integers and an integer modulus, do rational reconstruction on all entries of the matrix, viewed as numbers mod $N$ . This is done efficiently by assuming there is a large common factor dividing the denominators. (sagemath.org)
Here in the above code, we have a matrix of integer type. (tutorialspoint.com)

A tri-diagonal matrix is one with non-zero entries along the main diagonal, and one diagonal above and below the main one (see the figure). (sarawak.com.my)
The algorithm is designed to be extendable to higher order banded diagonal systems. (sarawak.com.my)
Most of those techniques focus on reducing the bandwidth of the matrix, which is defined as the furthest distance of a non-zero entry from the main diagonal. (stackexchange.com)
When you reorder the matrix, the main goal is to reduce the amount of fill in (banded matrices have almost no fill in, however, just one entry can really cause a lot of fill in if far from the diagonal). (stackexchange.com)
In this function, we run a for loop to iterate through each element of the given matrix and then find the sum of the primary and secondary diagonal. (tutorialspoint.com)

transformation, the original matrix is transformed in a ﬁnite numberof steps to Hessenberg form or - in the Hermitian/symmetric case - to real tridiagonal form. (sarawak.com.my)
1] An orthogonal transformation of a symmetric (or Hermitian) matrix to tridiagonal form can be done with the Lanczos algorithm. (sarawak.com.my)
On Symmetric Algorithms for Bilinear Forms over Finite Fields. (uni-trier.de)

This book marks the first appearance is an organized library of the algorithms for the eigenvalue problem for dense, stored matrices that we still use in MATLAB today. (mathworks.com)

Computing the determinant of such a matrix requires only (as opposed to ) arithmetic operations (Acton 1990, p. 332).Efficient solution of the matrix equation for , where is a tridiagonal matrix, can be performed in the Wolfram Language using LinearSolve on , represented as a SparseArray. (sarawak.com.my)
Efficient Algorithms for a Family of Matroid Intersection Problems. (uni-trier.de)
The state of the art in numerical linear algebra 50 years ago, in the 1960's, did not yet provide reliable, efficient methods for solving matrix eigenvalue problems. (mathworks.com)

Our algorithm has polynomial time complexity, and its computation time is reasonable even for relatively large networks. (aaai.org)

Two numerical examples are provided to show the effectiveness of the proposed algorithm. (ac.ir)

i need the matlab or c coding of those algorithm. (dsprelated.com)
Numerical experiments show that MATLAB implementations of this algorithm has higher accuracy than other MATLAB implementations of the state of the art in the majority of tests. (upv.es)
I found an implementation of the thomas algorithm or TDMA in MATLAB. (sarawak.com.my)

A new algorithm is presented, designed to solve tridiagonal matrix problems efficiently with parallel computers (multiple instruction stream, multiple data stream (MIMD) machines with distributed memory). (sarawak.com.my)
A Tridiagonal Matrix We investigate the simple n×n real tridiagonal matrix: M = ... We use recursion on n, the size of the n×n matrix T. It will be convenient to build on (1) and let D n = det(T −λI). (sarawak.com.my)
A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix… Then, expanding by minors using As before, write λ = 2c. (sarawak.com.my)
This ﬁrst stage of the algorithm prepares its second stage, the actual QR iterations that are applied to the Hessenberg or tridiagonal matrix. (sarawak.com.my)
LU decomposition of a tridiagonal matrix. (sarawak.com.my)
I'd like to calculate alpha-coefficients efficiently.The algorithm … The determinant of a tridiagonal matrix is given by the continuant of its elements. (sarawak.com.my)
The Tridiagonal Matrix Algorithm, also known as the Thomas Algorithm, is an application of gaussian elimination to a banded matrix. (sarawak.com.my)

It is experimentally shown that the proposed algorithm estimates the mixing matrix with high accuracy and robustness compared with existing algorithms. (yhxb.org.cn)
The Jacobian matrix (or the gradient for single-output networks) is directly related to many important properties of neural networks, such as the function landscape, stationary points, (local) Lipschitz constants and robustness to adversarial attacks. (aaai.org)

A variant of this algorithm that works for matrices of arbitrary shapes and is faster in practice splits matrices in two instead of four submatrices, as follows. (wikipedia.org)

Essentially, the constrained critical line algorithm incorporates its lambda constraints into the structure of the covariance matrix itself. (r-bloggers.com)

A Non-Factorial Algorithm for Canonical Numbering of a Graph. (uni-trier.de)

We can rule out algebraic algorithms like in Ryan Williams answer -- those perform the same number of steps regardless of numeric values. (stackexchange.com)
The algorithm, named harmonic variety-based matrix completion (HVMC), utilizes the fact that the points lying on the MEP of a reaction step constitute an algebraic variety in the reaction path Hamiltonian representation. (aip.org)

A binary dataset is a data matrix about the relationship between a set of objects[ 7 ]. (biomedcentral.com)
Please see the instruction on how to prepare dataset for the Two Matrix CIM . (nih.gov)

Additionally, we use our bounds of Jacobian matrix to characterize the landscape of the neural network, for example, to determine whether there exist stationary points in a local neighborhood. (aaai.org)
In all methods, the solution of the TRS involves solving a linear least squares system involving the Jacobian matrix. (gnu.org)
interface), this is accomplished by factoring the full Jacobian matrix, which is provided by the user, with the Cholesky, QR, or SVD decompositions. (gnu.org)
Constant-acceleration motion Jacobian, returned as a real-valued 3N -by- 3N matrix. (mathworks.com)

Matrix determinant. (stackexchange.com)
For matrix determinant it seems from this mathoverflow answer that $n^\omega$ is not even possible. (stackexchange.com)

2003). We improve their algorithm in terms of reliability by applying the augmented Lagrangian method and show in our numerical tests that the resulting algorithm yields better performance than other existing methods. (manchester.ac.uk)

There are generally two classes of algorithms for solving nonlinear least squares problems, which fall under line search methods and trust region methods. (gnu.org)

This work presents an algorithm based on Taylor series for computing the matrix cosine. (upv.es)

The Lyapunov matrix equation (or Sylvester Equation ) $A\Sigma + \Sigma A^T = R$ can be solved by the alternating-direction implicit (ADI) method. (stackexchange.com)
A similar problem of this matrix equation with generalized constrained is also discussed. (hindawi.com)
How to construct the matrix in the equation $Ax=b$ in the HHL algorithm? (stackexchange.com)

Scheduling of Agile Satellites Based on an Improved Quantum Genetic Algorithm [J]. Journal of Astronautics, 2018, 39(11): 1266-1274. (yhxb.org.cn)

The biclusters obtained by binary biclustering algorithms are considered to be submatrices with all 1. (biomedcentral.com)

The matrix $A$ is randomly generated Hermitian matrix, and may/may not be sparse (checking what happens, is also something I'm wondering). (stackexchange.com)

In the algorithm, the single source points in the time frequency (TF) domain are detected first. (yhxb.org.cn)
While other algorithm is achieved in frequency domain, our algorithm use simpler model for image perception and obtain the filter directly in the spatial domain. (korea.ac.kr)

Motivated by this success, we outline next steps toward developing a practical HVMC algorithm, which utilizes a gradient-based sampling protocol for low-cost VTST rate computations. (aip.org)

My intuition is that well conditioned matrices are in some sense trivial, and this should be a benefit, not just for linear solving, but also other matrix related problems. (stackexchange.com)
We call these problems structured matrix nearness problems. (manchester.ac.uk)
In this paper, we show that minimum-volume NMF (min-volNMF) can also be used when the basis matrix is rank deﬁcient, which is a reasonable scenario for some real-world NMF problems (e.g., for unmixing multispectral images). (researchgate.net)
To tackle these problems, we consider algorithms that are based primarily on coarsening techniques, possibly combined with random sampling. (ibm.com)

The user also has the ability to tune a number of parameters which affect low-level aspects of the algorithm which can help to accelerate convergence for the specific problem at hand. (gnu.org)

The algorithm fully considers the constraint relationship between users' attributes and nutritional characteristics of foods. (techscience.com)

We shall approach this using dynamic programming -- the greedy algorithm is 'myopic' in that it only considers immediate neighbors and not the path that follows those neighbors. (stackexchange.com)

The algorithm itself requires five parameters, each vectors. (sarawak.com.my)

A New Tracking Algorithm for Near Space Hypersonic Vehicle in Gliding Jumping Phase [J]. Journal of Astronautics, 2017, 38(9): 971-978. (yhxb.org.cn)
A Real Time SIFT Feature Extraction Algorithm [J]. Journal of Astronautics, 2017, 38(8): 865-871. (yhxb.org.cn)

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