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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A novel and faster quantum-inspired algorithm for solving linear systems
线性系统 新颖 量子衍生算法
2023/4/17
In this talk, we introduce a modified classical algorithm to solve linear systems in a model that resembles the QRAM used by quantum linear solvers. Specifically, we demonstrate that for the linear sy...
Cuts from Proofs: A Complete and Practical Technique for Solving Linear Inequalities Over Integers
Complete Practical Technique Linear Inequalities Over Integers
2016/5/24
We propose a novel, sound, and complete Simplex-based algorithm for solving linear inequalities over integers. Our algorithm, which can be viewed as a semantic generalization of the branch-and-bound t...
Solving Linear Equations Modulo Unknown Divisors: Revisited
Lattice-based analysis Linear modular equations RSA
2016/1/9
We revisit the problem of finding small solutions to a collection
of linear equations modulo an unknown divisor p for a known
composite integer N. In CaLC 2001, Howgrave-Graham introduced an
effici...
Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
Random Quadratic Systems Solving Linear Systems
2015/6/17
We consider the fundamental problem of solving quadratic systems of equations in n variables, where yi = |hai, xi|2, i = 1, . . . , m and x ∈ Rn is unknown. We propose a novel method, which starting w...
Solving Linear Differential Equations: A Novel Approach
Linear Differential Equations Novel Approach Mathematical Physics
2012/5/24
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the...
Quantum algorithms for solving linear differential equations
Quantum algorithms solving linear differential equations
2010/11/5
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by homogeneous linear differential equations that produce o...
Solving Linear Systems via Composition of their Clans
linear system decomposition clans acceleration of computation
2013/1/29
The decomposition technique for linear system solution is proposed. This technique may be combined with any known method of linear system solution. An essential acceleration of computations is obtaine...
A new method for solving fuzzy linear programming by solving linear programming
Fuzzy arithmetic Fuzzy linear programming Fuzzy number
2010/9/14
A new method for solving fuzzy linear programming by solving linear programming.
A new column recurrence algorithm based on the classical Greville method and
modified Huang update is proposed for computing generalized
inverse matrix and least squares solution. The numerical resu...