• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.927-931
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• 2003

In this paper, a new Recursive Least-Squares(RLS) algorithm based on matrix pseudo-inverses is presented. The aim is to use the proposed new RLS algorithm for not only the over-determined but also the under-determined estimation problem. Compared with previous results, e.g., Jie Zhou et al., the derivation of the proposed recursive form is much easier, and the recursion form is also much simpler. Furthermore, it is shown by simulations that the proposed RLS algorithm is more efficient and numerically stable than the existing algorithms.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.849-857
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• 1998

In this paper we have a concern on the Moore-Penrose inverse of two kinds of partitioned matrices of the form [V X] and [{{{{ {V atop {X} {{{{ {X atop { 0} }}] where V is symmetric. The Moore-Penrose inverse of the partitioned matrices can be reduced to be simpler forms according to some algebraic conditions. Firstly we investigate the representations of the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Morre-Penrose inverse into some simpler form. Also equivalant conditions will be considered. Finally we will perform a simulation study to investigate which con-dition is the most important in the sense that which condition occurs the most frequently in the real situation. The simluation study will show us a particular condition occurs the most likely tha other conditions. This fact enables us to obtain the Morre-Penrose inverse with less computational efforts and computational storage.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.343-352
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• 2013

In this paper, we give a formula of $(P+Q)^D$ under the conditions $P^2Q+QPQ=0$ and $P^3Q=0$. Then applying it to give some results of block matrix $M=(^A_C^B_D)$ (A and D are square matrices) with generalized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.409-418
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• 2016

In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1011-1020
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• 2008

The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.605-616
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• 2003

In this paper, some rank equalities related to generalized inverses $A^{(2)}_{T,S}$ of a matrix are presented. As applications, a variety of rank equalities related to the M-P inverse, the Drazin inverse, the group inverse, the weighted M-P inverse, the Bott-Duffin inverse and the generalized Bott-Duffin inverse are established.

• 대한수학회논문집
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• 제33권3호
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• pp.695-704
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• 2018

In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.

• 대한수학회지
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• 제46권6호
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• pp.1139-1150
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• 2009

We obtain necessary and sufficient conditions for $2{\tims}2$ block operator valued matrices to be Moore-Penrose (MP) invertible and give new representations of such MP inverses in terms of the individual blocks.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.177-193
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• 2010

Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type $F_n(x)=\sum\limits_{k=0}^{n}A^n_kG_k(x)$ and $ G_n(x)=\sum\limits_{k=0}^{n}B_k^nF_k(x)$, where 0, 1, 2,$\cdots$. Here $F_n(x)$, $G_n(x)$ denote special polynomial functions, and $A_k^n$, $B_k^n$ denote coefficients found by use of the orthogonal properties of $F_n(x)$ and $G_n(x)$, or by skillful series manipulations. Typically $G_n(x)=x^n$ and $F_n(x)=P_n(x)$, the n-th Legendre polynomial. We give a collection of inverse series pairs of the type $f(n)=\sum\limits_{k=0}^{n}A_k^ng(k)$ if and only if $g(n)=\sum\limits_{k=0}^{n}B_k^nf(k)$, each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.

• 충청수학회지
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• 제29권2호
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• pp.267-281
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• 2016

In this paper, we consider multi-degree reduction of $B{\acute{e}}zier$ curves with continuity of any (r, s) order with respect to $L_2$ norm. With help of matrix theory about generalized inverses we can use Lagrange multipliers to obtain the degree reduction matrix in a very simple form as well as the degree reduced control points. Also error analysis comparing with the least squares degree reduction without constraints is given. The advantage of our method is that the relationship between the optimal multi-degree reductions with and without constraints of continuity can be derived explicitly.