Proposes several methods to compute the exponential of a matrix. Factors considered in assessing the effectiveness of various algorithms; Characteristics of a reliable algorithm; Common theme of series methods; Potential causes of a large error estimate; Properties of companion matrices.Moler...
Nineteen Dubious Ways to Compute the exponential of a matrix, twenty-five years later Moler & Van Loan 的经典论文,关于矩阵指数计算的Review 第二版Moler & Van Loan 的经典论文,关于矩阵指数计算的Review 第二版隐藏>> SIAM REVIEW Vol. 45, No. 1, pp. 3–49 c 2003 Society for Industrial and ...
In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency indicates that ...
An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system. Journal of App. Alg. in Eng. Comm. and Comp., 8(1):1- 23, 1997.M. A. Barkatou. An algorithm to compute the exponential part of a formal fundamental matrix solution of...
It is pretty common to want to compute unitary matrix exponentials of the form $e^{iAt}b$ for Hermitian matrices $A$. It would be nice to have a method that takes advantage of $A$ being Hermitian here, and right now this doesn't seem to ...
Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenv... C Moler,C Van Loan - 《Siam Review》 被引量: ...
Also:Google says 'exponential' growth of AI is changing nature of compute And the pace of demand for compute cycles is increasingly sharply. According todata from OpenAI, the venerable AlexNet image recognition system, created way back in 2012, consumed the equivalent of one thousand trillion floa...
From the above definition we see that the eigenvalues of the matrix are the solutions to the equation: det(A−λI)=0 The polynomialp(λ)=det(A−λI)is called the characteristic polynomial of the matrix and its zeros are the...
println(cachedTensor.toString) val tmp: InlineTensor = exp(cachedTensor) // The cache for cachedTensor is reused, but the exponential function is performed. println(tmp.toString) // The cache for cachedTensor is reused, but the exponential function is performed, again. println(tmp.toString) }...
(-1,3);// automatic shape detectionlety =Vector::from([1.,2.,3.]);// vector structletpd = x.t().dot(x);// transpose and matrix multiplyletjitter =Matrix::eye(3)*1e-6;// elementwise operationsletc =(pd + jitter).cholesky();// matrix decompositionslets = c.solve(&y.exp(...