Background: To understand the status of residents' awareness of and demand for hospice care services in Hangzhou and to provide a reference for promoting the formulation of hospice care-related policies in China. Methods: A small cross-sectional survey of 519 adults aged over 40 years old living in the rural-urban fringe and urban area of Xihu District, Hangzhou City, was conducted using convenience sampling and a self-designed questionnaire. The measures assessed awareness of hospice care (13-item scale), attitudes towards life support therapy (3-item scale), and demand for hospice care services (9-item scale). Results: The rate of awareness of hospice care among community residents was 50.30%. A total of 51.0% of residents wanted only comfortable life-sustaining treatment at the end of their lives. The acceptance of hospice care was positively correlated with the degree of understanding (x 2 = 18.382, P = 0.001), and residents in the urban area were more likely to prefer hospice care than residents in the urban-rural fringe (x 2 = 7.186, P = 0.028). Elderly residents showed a stronger tendency to prefer comfortable life support therapy (x 2 = 12.988, P < 0.001). A total of 83.04% of the residents accepted the current necessity for hospice care to be provided in medical institutions. The preferred locations were professional hospice care institutions or general hospitals. A total of 93.64% of the residents agreed that the number of beds in hospice care wards should not exceed 2. In addition, the residents could afford part of the out-of-pocket expenses for hospice care services, with the ability to pay under 200 yuan per day, and the improvement of facilities was expected. Conclusions: To improve public awareness and acceptance of hospice care and promote healthy development in China, it is necessary to promote hospice care education for everyone.

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We consider the convergence problem of an inexact Cayley transform method for solving inverse eigenvalue problems with multiple eigenvalues. Under the nonsingularity assumption of the relative generalized Jacobian matrix at the solution c*, a convergence analysis covering both the distinct and multiple eigenvalues cases is provided and the superlinear convergence is proved. Moreover, numerical experiments are given in the last section and comparisons with the Cayley transform method are made.

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Inverse eigenvalue and singular value problems have been widely discussed for decades. The well-known result is the Weyl-Horn condition, which presents the relations between the eigenvalues and singular values of an arbitrary matrix. This result by Weyl-Horn then leads to an interesting inverse problem, i.e., how to construct a matrix with desired eigenvalues and singular values. In this work, we do that and more. We propose an eclectic mix of techniques from differential geometry and the inexact Newton method for solving inverse eigenvalue and singular value problems as well as additional desired characteristics such as nonnegative entries, prescribed diagonal entries, and even predetermined entries. We show theoretically that our method converges globally and quadratically, and we provide numerical examples to demonstrate the robustness and accuracy of our proposed method. Having theoretical interest, we provide in the appendix a necessary and sufficient condition for the existence of a 2 × 2 real matrix, or even a nonnegative matrix, with prescribed eigenvalues, singular values, and main diagonal entries.Mathematics Subject Classification (2010) 15A29 · 65H17.Keywords Inverse eigenvalue and singular value problems, nonnegative matrices, Riemannian inexact Newton method.