n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

We are often required to retouch images in order to improve their visual appearance, by removing the visual discontinuities like breaks and damaged regions. Such retouching of images may be achieved by inpainting. Current techniques for image inpainting require the user to manually select the target regions to be inpainted. Very few techniques for automatically detecting the target regions for ...

Let A be an m × n matrix with m ≥ n. Then one form of the singular-value decomposition of A is A = UΣV, where U and V are orthogonal and Σ is square diagonal. That is, UUT = Irank(A), V V T = Irank(A), U is rank(A)×m, V is rank(A)× n and Σ =   σ1 0 · · · 0 0 0 σ2 · · · 0 0 .. .. . . . .. .. 0 0 · · · σrank(A)−1 0 0 0 · · · 0 σrank(A)   is a rank(A)× rank(A) diagonal matrix. In add...

In this paper, we propose a practical method to reduce a number of reference signals for the active noise cancellation (ANC) system and the filter characteristics to generate the reduced number of reference signals, which maintain the original value of the coherence function. This method finds the number of independent noise sources and provides the filter characteristics based on SVD (singular...

Part (a) of the claim was proved in Recht et al. [2]; we simply provide a proof here for completeness. We write the SVD as Θ∗ = UDV T , where U ∈ Rm1×m1 and V ∈ Rm2×m2 are orthogonal matrices, and D is the matrix formed by the singular values of Θ∗. Note that the matrices U r and V r are given by the first r columns of U and V respectively. We then define the matrix Γ = UTΔV ∈ Rm1×m2 , and writ...

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r , find a matrix A ∈ Rn×n such that ‖XTAX − B‖ = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n× n matrix à with Ã([1, r])...

− The steady state data reconciliation problem is approached via a geometrical picture of its model and measurement abstract spaces. By completely utilizing the structure of the problem constraint matrix, via its singular value decomposition (SVD), data adjustment is accomplished and redundancy and observability conditions are formulated. As an example, the method is applied to a small network ...

The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and then show the central role of SVD in matrices. Using majorization theory, we consider variational principles of singular values and eigenvalues. Built on SVD...