On the basis of the conversion relation of inverse matrix and adjoint matrix, by using 1/ω instead of |B'(xBx(subscript k|, a new Landweber iteration formula x(superscript δ subscript k+1)=x(superscript δ subscript k)-ωB'(x(superscript δ subscript k)Bx(superscript δ subscript kB'x(superscript δ kf(x(superscript δ subscript k)-y(superscript δ)is constructed for solving rank deficiency nonlinear least squares problem, with which the phenomenon that leads to ill-posed problem because the iteration matrix is rank-deficient and very ill-conditioned in numerical iterative process is avoided.

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Be ill in bed 臥病在床 He was ill in bed all day yesterday.

他昨天一整天臥病在床。

I have enteritis this afternoon,I feel ill.after eat some medicine,I feel better.although I had noticed food and water must be cleanlily,but I have ill for my stomach..

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Beginning with some cases, the article gives basic definitions of inverse problems and ill-posed problems. Then it discusses the Moore-Penrose generalized solution and the Moore-Penrose generalized inverse, and makes a conclusion that linear compact operator equations are ill-posed, that is, the Moore-Penrose generalized solution is unstable.

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In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

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Order Hilbert ill-conditioned linear equations were solved, and the relative error was less than 0.45%. Numerical experiments verified that the method was efficient compared with the efficient methods used commonly nowadays. Numerical experiments results showed that the conjugate vector base method was suited for solving large-scale ill-conditioned linear equations with fast convergence and high precision.

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So spake the false dissembler unperceivd; For neither Man nor Angel can discern Hypocrisie, the onely evil that walks Invisible, except to God alone, By his permissive will, through Heav'n and Earth: [ 685 ] And oft though wisdom wake, suspicion sleeps At wisdoms Gate, and to simplicitie Resigns her charge, while goodness thinks no ill Where no ill seems: Which now for once beguil'd Uriel, though Regent of the Sun, and held [ 690 ] The sharpest sighted Spirit of all in Heav'n; Who to the fraudulent Impostor foule In his uprightness answer thus returnd.

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