[1]
Babuska, I., Nobile, F. and Tempone, R., A stochastic collocation method for elliptic partial differential equations with random input data, SIAM Review, 52(2) (2010), pp. 317–355.

[3]
Cai, T., Wang, L. and Xu, G., New bounds for restricted isometry constants, IEEE T. Inform. Theory, 56 (2010), pp. 4388–4394.

[4]
Cai, T., Wang, L. and Xu, G., Shifting inequality and recovery of sparse signals, IEEE T. Signal Proces., 58 (2010), pp. 1300–1308.

[5]
Candès, E., Rudelson, M., Tao, T. and Vershynin, R., Error correction via linear programming, in Proceeding of the 46th Annual IEEE Symposium on Foundations of Computer Science, 2005, pp. 668–681.

[6]
Candès, E. J., The restricted isometry property and its implications for compressed sensing, C. R. Acad. Sci. Paris Sér. I Math., 346 (2008), pp. 589–592.

[7]
Candès, E. J., Romberg, J. and Tao, T., Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math., 56 (2006), pp. 1207–1223.

[8]
Candès, E. J. and Tao, T., Decoding by linear programming, IEEE T. Inform. Theory, 51 (2005), pp. 4203–4215.

[9]
Davies, M. E. and Gribonval, R., Restricted isometry constants where ℓ_{p} sparse recovery can fail for 0 < p ≤ 1, IEEE T. Inform. Theory, 55 (2010), pp. 2203–2214.

[10]
Donoho, D. L., Compressed sensing, IEEE T. Inform. Theory, 52 (2006), pp. 1289–1306.

[11]
Doostan, A. and Owhadi, H., A non-adapted sparse approximation of pdes with stochastic inputs, J. Comput. Phys, 230 (2011), pp. 3015–3034.

[12]
Ernst, O. G., Mugler, A., Starkloff, H. J. and Ullmann, E., On the convergence of generalized polynomial chaos expansions, ESAIM: Mathematical Modelling and Numerical Analysis, 46(2) (2012), pp. 317–339.

[13]
Foucart, S. and Lai, M. J., Sparsest solutions of undetermined linear systems via ℓ_{q}-minimization for 0 < q ≤ 1, Appl. Comput. Harmon. Anal., 26 (2009), pp. 395–407.

[14]
Gao, Z. and Zhou, T., On the choice of design points for least square polynomial approximations with application to uncertainty quantification, Commun. Comput. Phys., 16 (2014), pp. 365–381.

[15]
Guo, L., Narayan, A., Zhou, T. and Chen, Y., Stochastic collocation methods via ℓ1 minimization using randomized quadratures, SIAM J. Sci. Comput., 39-1 (2017), pp. A333–A359.

[16]
Hsia, Y. and Sheu, R. L., On RIC Bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using *ℓ*_{q}
Quasi Norms, Mathematics, 2013.

[17]
Jakeman, J., Narayan, A. and Zhou, T., A generalized sampling and preconditioning scheme for sparse approximation of polynomial chaos expansions, SIAM J. Sci. Comput., 39-3 (2017), pp. A1114–A1144.

[18]
Lai, M. J. and Wang, J., An unconstrained ℓ_{q} minimization for sparse solution under determined linear systems, SIAM J. Optimization, 21 (2011), pp. 82–101.

[19]
Liu, Y. L. and Guo, L., Stochastic collocation via l1-minimisation on low discrepancy point sets with application to uncertainty quantification, East Asian J. Appl. Math., 6 (2016), pp. 171–191.

[20]
Liu, W. H., Gong, D. and Xu, Z., One-Bit compressed sensing by greedy algorithms, Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 169–184.

[21]
Mathelin, L. and Gallivan, K. A., A compressed sensing approach for partial differential equa- tions with random input data, Commun. Comput. Phys., 12 (2012), pp. 919–954.

[22]
Narayan, A. and Zhou, T., Stochastic collocation methods on unstructured meshes, Commun. Comput. Phys., 18 (2015), pp. 1–36.

[23]
Rauhut, H. and Ward, R., Sparse legendre expansions via ℓ_{1}-minimization, J. Approx. Theory, 164 (2012), pp. 517–533.

[24]
Shu, R. W., Jin, J. W. and Jin, S., A stochastic Galerkin method for the Boltzmann equation with multi-dimensional random inputs using sparse Wavelet bases, Numer. Math. Theor. Meth. Appl., 10(2) (2017), pp. 465–488.

[25]
Song, C. B. and Xia, S. T., Sparse signal recovery by ℓ_{q} minimization under restricted isometry property, IEEE Signal Proc. Let., 21(9) (2014), pp. 1154–1158.

[26]
Tang, T. and Zhou, T., Recent developments in high order numerical methods for uncertainty quantification, Science in China: Mathematics, 45(7) (2015), pp. 891–928.

[27]
Xiu, D., Efficient collocational approach for parametric uncertainty analysis, Commun. Comput. Phys., 2 (2007), pp. 293–309.

[28]
Xiu, D., Fast numerical methods for stochastic computations: a review, Commun. Comput. Phys., 5 (2009), pp. 242–272.

[29]
Xiu, D. and Karniadakis, G. E., The wiener-askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), pp. 619–644.

[30]
Xu, Z. and Zhou, T., On sparse interpolation and the design of deterministic interpolation points, SIAM J. Sci. Comput., 36 (2014), pp. A1752–A1769.

[31]
Yan, L., Guo, L. and Xiu, D., Stochastic collocation algorithms using ℓ_{1} minimization, Int. J. Uncertain Quantification, 2 (2012), pp. 279–293.

[32]
Yan, L., Shin, Y. and Xiu, D., Sparse approximation using ℓ_{1}–ℓ_{2} minimization and its applications to stochastic collocation, SIAM J. Sci. Comput., 39(1) (2017), pp. A229–A254.