In[1], it is shown that Tony Chan’s circulant approximation ofn×nmatrixAhas the formcircF(A)=F*δ(FAF*)F. This idea of finding the optimal Frobenius norm approximation ofAusingFourier matrixhas been extended in[10]using anyn×nunitary matrix. In[2], it is further extended using bl...
When using Mathematica, the routine MatrixExp[, ] gives the result directly in terms of RootSum[, ]. The three diagonal generators are λ3=diag(1,−1,0,0),λ8=diag(1,1,−2,0)/3, and λ15=diag(1,1,1,−3)/6. The remaining 12 generators have two non-zero entries either ...
x=sin(2*pi*20*t-e);plot(t,x)提示：Inner matrix dimensions must agree.Error in ==> ...
This is easily done using a different form of the sparse function. This time the function is supplied with the location of the non-zero entries in the matrix, the value of these entries, the size of the sparse matrix and the space allocated for the non-zero entries. This function call ...
A CAL tutor for matrix theory is presented in this paper, in the form of Mathematica Notebooks. This constitutes one of a list of specific A-level mathematics core options required by science and engineering departments. The module has been written so as to recognize students errors and advise...
Linear independence of monomials of multizeta values in positive characteristic. In this paper, we study transcendence theory for Thakur multizeta values in positive characteristic. We prove an analogue of the strong form of Goncharov's... Chang,Chieh-Yu - 《Compositio Mathematica》 被引量: 30发...
本文主要探讨了有理矩阵指数的计算问题,其最重要的成果是结合符号计算推出了一种计算有理矩阵指数的新方法,利用该方法可以给出有理矩阵指数的一类精确表达式,还可以利用Mathematica软件给出十万位以内任意精度的数值结果。 更多例句>> 3) rational canonical form of matrix ...
Clearly the adjoint method changes the problem of inverting a general square matrix to determining its determinant and adjoint form. We now consider these aspects for general m. Consider a general m × m matrix, A = [aij]. As we will see, both det(A) and adj(A) are defined in terms...
A n-by-n matrix is a Toeplitz matrix if the elements in the first row and the first column are successive integers. The ToeplitzMatrix function built into Mathematica can be used to create Toeplitz matrices. Illustration ■ A 4-by-4 Toeplitz matrix MatrixForm[T = ToeplitzMatrix[4]] 12342123...
In this section, we perform error estimation of the approximation solution to find the error boundaries of the new numerical approach by applying the Genocchi polynomials. Consider the nonlinear Volterra integral equations with weakly singular kernels of the form Equation (1), We suppose that Ω =...