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Numerical linear algebra is a very important topic in mathematics and has important recent applications in deep learning, machine learning, image processing, applied statistics, artificial intelligence and other interesting modern applications in many fields. The purpose of this Special Issue in Mathematics is to present the latest contributions and recent developments in numerical linear algebra and applications in different real domains. We invite authors to submit original and new papers and high-quality reviews related to the following topics: applied linear algebra, linear and nonlinear systems of equations, large matrix equations, numerical tensor problems with applications, ill-posed problems and image processing, linear algebra and applied statistics, model reduction in dynamic systems, and other related subjects. The submitted papers will be reviewed in line with the traditional submission process. This Special Issue will be dedicated to the inspired mathematician Constantin Petridi, who has devoted his life to mathematics.

Information technology industries --- inverse scattering --- reciprocity gap functional --- chiral media --- mixed boundary conditions --- non-linear matrix equations --- perturbation bounds --- Lyapunov majorants --- fixed-point principle --- nonsymmetric differential matrix Riccati equation --- cosine product --- Golub–Kahan algorithm --- Krylov subspaces --- PCA --- SVD --- tensors --- quadratic form --- estimates --- upper bounds --- networks --- perron vector --- power method --- lanczos method --- pseudospectra --- eigenvalues --- matrix polynomial --- perturbation --- Perron root --- large-scale matrices --- approximation algorithm --- high-dimensional --- minimum norm solution --- regularisation --- Tikhonov --- ℓp-ℓq --- variable selection --- inverse scattering --- reciprocity gap functional --- chiral media --- mixed boundary conditions --- non-linear matrix equations --- perturbation bounds --- Lyapunov majorants --- fixed-point principle --- nonsymmetric differential matrix Riccati equation --- cosine product --- Golub–Kahan algorithm --- Krylov subspaces --- PCA --- SVD --- tensors --- quadratic form --- estimates --- upper bounds --- networks --- perron vector --- power method --- lanczos method --- pseudospectra --- eigenvalues --- matrix polynomial --- perturbation --- Perron root --- large-scale matrices --- approximation algorithm --- high-dimensional --- minimum norm solution --- regularisation --- Tikhonov --- ℓp-ℓq --- variable selection

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Numerical linear algebra is a very important topic in mathematics and has important recent applications in deep learning, machine learning, image processing, applied statistics, artificial intelligence and other interesting modern applications in many fields. The purpose of this Special Issue in Mathematics is to present the latest contributions and recent developments in numerical linear algebra and applications in different real domains. We invite authors to submit original and new papers and high-quality reviews related to the following topics: applied linear algebra, linear and nonlinear systems of equations, large matrix equations, numerical tensor problems with applications, ill-posed problems and image processing, linear algebra and applied statistics, model reduction in dynamic systems, and other related subjects. The submitted papers will be reviewed in line with the traditional submission process. This Special Issue will be dedicated to the inspired mathematician Constantin Petridi, who has devoted his life to mathematics.

inverse scattering --- reciprocity gap functional --- chiral media --- mixed boundary conditions --- non-linear matrix equations --- perturbation bounds --- Lyapunov majorants --- fixed-point principle --- nonsymmetric differential matrix Riccati equation --- cosine product --- Golub–Kahan algorithm --- Krylov subspaces --- PCA --- SVD --- tensors --- quadratic form --- estimates --- upper bounds --- networks --- perron vector --- power method --- lanczos method --- pseudospectra --- eigenvalues --- matrix polynomial --- perturbation --- Perron root --- large-scale matrices --- approximation algorithm --- high-dimensional --- minimum norm solution --- regularisation --- Tikhonov --- ℓp-ℓq --- variable selection

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Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms.

Research & information: general --- Mathematics & science --- forgotten index --- balaban index --- reclassified the zagreb indices --- ABC4 index --- GA5 index --- HDN3(m) --- THDN3(m) --- RHDN3(m) --- degree of vertex --- extended adjacency index --- scheduling with rejection --- machine non-availability --- operator non-availability --- dynamic programming --- FPTAS --- Transportation --- batching scheduling --- total weighted completion time --- unary NP-hard --- approximation algorithm --- bi-criteria scheduling --- online algorithm --- makespan --- maximum machine cost --- competitive ratio --- network optimization --- dynamic flow --- evacuation planning --- contraflow configuration --- partial lane reversals, algorithms and complexity --- logistic supports --- scheduling algorithm --- release-time --- due-date --- divisible numbers --- lateness --- bin packing --- time complexity --- batch scheduling --- linear deterioration --- job families --- Max-cut problem --- combinatorial optimization --- deep learning --- pointer network --- supervised learning --- reinforcement learning --- capacitated lot sizing --- mixed integer formulation --- retail --- inventory --- shortages --- graph --- join product --- crossing number --- cyclic permutation --- arithmetic mean --- combinatorial generation --- method --- algorithm --- AND/OR tree --- Euler-Catalan's triangle --- labeled Dyck path --- ranking algorithm --- unranking algorithm --- Harris hawks optimizer --- load frequency control --- sensitivity analysis --- smart grid --- particle swarm optimization --- genetic algorithm --- meta-heuristics --- packing --- irregular 3D objects --- quasi-phi-function s --- nonlinear optimization --- single-machine scheduling --- minimization of maximum penalty --- dual problem --- inverse problem --- branch and bound --- LNS --- numerical conversion --- RISC --- FPGA --- embedded systems --- scheduling --- job-shop --- makespan criterion --- uncertain processing times --- forgotten index --- balaban index --- reclassified the zagreb indices --- ABC4 index --- GA5 index --- HDN3(m) --- THDN3(m) --- RHDN3(m) --- degree of vertex --- extended adjacency index --- scheduling with rejection --- machine non-availability --- operator non-availability --- dynamic programming --- FPTAS --- Transportation --- batching scheduling --- total weighted completion time --- unary NP-hard --- approximation algorithm --- bi-criteria scheduling --- online algorithm --- makespan --- maximum machine cost --- competitive ratio --- network optimization --- dynamic flow --- evacuation planning --- contraflow configuration --- partial lane reversals, algorithms and complexity --- logistic supports --- scheduling algorithm --- release-time --- due-date --- divisible numbers --- lateness --- bin packing --- time complexity --- batch scheduling --- linear deterioration --- job families --- Max-cut problem --- combinatorial optimization --- deep learning --- pointer network --- supervised learning --- reinforcement learning --- capacitated lot sizing --- mixed integer formulation --- retail --- inventory --- shortages --- graph --- join product --- crossing number --- cyclic permutation --- arithmetic mean --- combinatorial generation --- method --- algorithm --- AND/OR tree --- Euler-Catalan's triangle --- labeled Dyck path --- ranking algorithm --- unranking algorithm --- Harris hawks optimizer --- load frequency control --- sensitivity analysis --- smart grid --- particle swarm optimization --- genetic algorithm --- meta-heuristics --- packing --- irregular 3D objects --- quasi-phi-function s --- nonlinear optimization --- single-machine scheduling --- minimization of maximum penalty --- dual problem --- inverse problem --- branch and bound --- LNS --- numerical conversion --- RISC --- FPGA --- embedded systems --- scheduling --- job-shop --- makespan criterion --- uncertain processing times

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This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience. The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.

Traveling salesman problem. --- TSP (Traveling salesman problem) --- Combinatorial optimization --- Graph theory --- Vehicle routing problem --- AT&T Labs. --- Accuracy and precision. --- Addition. --- Algorithm. --- Analysis of algorithms. --- Applied mathematics. --- Approximation algorithm. --- Approximation. --- Basic solution (linear programming). --- Best, worst and average case. --- Bifurcation theory. --- Big O notation. --- CPLEX. --- CPU time. --- Calculation. --- Chaos theory. --- Column generation. --- Combinatorial optimization. --- Computation. --- Computational resource. --- Computer. --- Connected component (graph theory). --- Connectivity (graph theory). --- Convex hull. --- Cutting-plane method. --- Delaunay triangulation. --- Determinism. --- Disjoint sets. --- Dynamic programming. --- Ear decomposition. --- Engineering. --- Enumeration. --- Equation. --- Estimation. --- Euclidean distance. --- Euclidean space. --- Family of sets. --- For loop. --- Genetic algorithm. --- George Dantzig. --- Georgia Institute of Technology. --- Greedy algorithm. --- Hamiltonian path. --- Hospitality. --- Hypergraph. --- Implementation. --- Instance (computer science). --- Institute. --- Integer. --- Iteration. --- Linear inequality. --- Linear programming. --- Mathematical optimization. --- Mathematics. --- Model of computation. --- Neuroscience. --- Notation. --- Operations research. --- Optimization problem. --- Order by. --- Pairwise. --- Parameter (computer programming). --- Parity (mathematics). --- Percentage. --- Polyhedron. --- Polytope. --- Pricing. --- Princeton University. --- Processing (programming language). --- Project. --- Quantity. --- Reduced cost. --- Requirement. --- Result. --- Rice University. --- Rutgers University. --- Scientific notation. --- Search algorithm. --- Search tree. --- Self-similarity. --- Simplex algorithm. --- Solution set. --- Solver. --- Source code. --- Special case. --- Stochastic. --- Subroutine. --- Subsequence. --- Subset. --- Summation. --- Test set. --- Theorem. --- Theory. --- Time complexity. --- Trade-off. --- Travelling salesman problem. --- Tree (data structure). --- Upper and lower bounds. --- Variable (computer science). --- Variable (mathematics).

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Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms.

Research & information: general --- Mathematics & science --- forgotten index --- balaban index --- reclassified the zagreb indices --- ABC4 index --- GA5 index --- HDN3(m) --- THDN3(m) --- RHDN3(m) --- degree of vertex --- extended adjacency index --- scheduling with rejection --- machine non-availability --- operator non-availability --- dynamic programming --- FPTAS --- Transportation --- batching scheduling --- total weighted completion time --- unary NP-hard --- approximation algorithm --- bi-criteria scheduling --- online algorithm --- makespan --- maximum machine cost --- competitive ratio --- network optimization --- dynamic flow --- evacuation planning --- contraflow configuration --- partial lane reversals, algorithms and complexity --- logistic supports --- scheduling algorithm --- release-time --- due-date --- divisible numbers --- lateness --- bin packing --- time complexity --- batch scheduling --- linear deterioration --- job families --- Max-cut problem --- combinatorial optimization --- deep learning --- pointer network --- supervised learning --- reinforcement learning --- capacitated lot sizing --- mixed integer formulation --- retail --- inventory --- shortages --- graph --- join product --- crossing number --- cyclic permutation --- arithmetic mean --- combinatorial generation --- method --- algorithm --- AND/OR tree --- Euler–Catalan’s triangle --- labeled Dyck path --- ranking algorithm --- unranking algorithm --- Harris hawks optimizer --- load frequency control --- sensitivity analysis --- smart grid --- particle swarm optimization --- genetic algorithm --- meta-heuristics --- packing --- irregular 3D objects --- quasi-phi-function s --- nonlinear optimization --- single-machine scheduling --- minimization of maximum penalty --- dual problem --- inverse problem --- branch and bound --- LNS --- numerical conversion --- RISC --- FPGA --- embedded systems --- scheduling --- job-shop --- makespan criterion --- uncertain processing times --- n/a --- Euler-Catalan's triangle